[EM] Re: Strong Favourite Betrayal Criterion at last!

[Chris Benham]

Forest,
My answer to your question Is there a simpler method that factors allof 
the strategy away from the rankings or ratings of the candidates? is 
yes. Voters can rank  and also Approve whichever candidates they please, 
not even neccessarily Approving the candidate they rank as number1.
The method  is to have an IRV-like count, except that the candidates who 
are in turn eliminated are those who are the least Approved.
For example, in a 3 candidate race in which you doubt that  Favourite 
can beat Worst  in a runoff, you might number the candidates  1. 
Favourite  2. Middle  3. Worst  , but  only  Approve Middle .
Chris Benham


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Re: [Election-Methods] Article about voting methods in Pasadena Weekly

[Chris Benham]

Steve,

I am very strongly of the view that the results of elections should as 
far as possible be determined purely
by voters voting. I hate schemes that encourage (or much worse, force) 
voters to pick some predetermined
ranking and/or have (after the votes have been cast) the machinations of 
candidates as part of the process
of deciding the winner.

I also think that the method should try to give all voters equal power. 
In VPR, the voters who are also
candidates and so get to publish a ranking and force the other voters 
to vote one of those published
rankings obviously have a lot more power than the non-candidate voters.

Further I think it is an excellent principle that all candidates on the 
ballot should have an equal chance
(subject only to voted support of voters) of winning. In VPR candidates 
that are low on other candidates'
published rankings clearly have less chance of winning than the others.



Steve Eppley wrote:

 Several years ago, Mike Alvarez of Caltech pointed out a risk of 
 preference-order voting: Some voters may fail
 to rank needed compromises when many candidates compete. Here's a 
 voting method that solves that problem:


Why is that a problem? How do you justify/explain your use of the word 
needed?


 Australia provides a shortcut similar to VPR in many elections: Prior 
 to Election Day, each party publicly ranks the candidates.
 Each voter may either tediously rank the candidates or select a party 
 — effectively voting that party's ranking. Most Australians
 use the shortcut.


The elections referred to here are all multi-winner PR elections. 
Everyone in the Australian PR society (and others in the STV-PR
movement) rightly regard the shortcut (called above-the-line voting) 
as an abomination that should be got rid of. Likewise they
are opposed to compulsion to rank all (or many) of the candidates.

 Voting for a Published Ranking (VPR):
 (1) During the weeks before Election Day, each candidate publishes a 
 ranking of all the candidates.

 (2) On Election Day, each voter selects a candidate.

 (3) The votes are published. Then the candidates are given a few days 
 to decide whether to withdraw.

 (4) Remove the withdrawn candidates from every ranking, so they won't 
 be spoilers. (Assume Obama
 ranked himself on top and Clinton second. Assume Obama withdraws. His 
 ranking will now have Clinton on top.)

 (5) Count each voter for the candidate atop the voter's selected 
 candidate's ranking. Elect the candidate with the
 largest count. (Count for Clinton the 33 percent who voted for Obama, 
 since she now tops Obama's ranking. Also
 count for Clinton the 27 percent who voted for her, giving her 60 
 percent. Clinton wins.)



Yuck!

 (3) The votes are published. Then the candidates are given a few days 
 to decide whether to withdraw. 


Why on earth should candidates be burdened with having to decide that? 
This process is obviously very
prone to corruption and arm-twisting.


 Another advantage: The best compromise candidates would not need as 
 much money to win, since they'd primarily need to
 persuade a small number of other candidates, not a mass of 
 disinterested voters.


Presumably under this scheme a lot more people would want to be 
candidates. Of course we could save a lot of money
and bother by taking it completely out of the hands of a mass of 
disinterested voters and just have a small number
of people decide who fills the office.


Chris Benham




Hi,

The current issue of the Pasadena Weekly, also available at 
www.pasadenaweekly.com, includes an article I wrote.  It shows how 
spoiling can occur given Instant Runoff (IRV), contrary to the beliefs 
of most IRV proponents.  It proposes several better methods, including a 
simple but probably very effective patch for IRV: letting candidates 
withdraw after the votes are cast.

I had nothing to do with the title  subtitle given the article by the 
Pasadena Weekly:
   Robert's Rules for voting
   Or Would VPR - not - IRV - elections be a better fit for Americans?

Regards,
Steve

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Re: [Election-Methods] Fwd: RE : Corrected strategy in Condorcet section, Chris

[Chris Benham]

Kevin Venzke wrote:

I think a better method that would achieve everything you are  
trying to do with your method (technically

if not psychologically) would be this:

1) Voters indicate one Favourite and also Approve as many  
candidates as they like.


2) Any candidate voted as favourite on 50% or more of the ballots  
wins.


3) Eliminate any candidate whose max. approval opposition score is  
greater than 50%, unless that is all

the candidates.  [I'm not sure if that's possible].
 



Nope, that's not possible. You can only get this score if someone else
has majority approval and you don't. It's an MD filter really.

 

4) Of the remaining candidates, the two voted as favourite on the  
most ballots go to the second round.


This uses a more expressive ballot and mainly confines the split- 
vote problem to the top of the ballot.
So the normal recommended strategy in the 3 viable candidates  
scenario would be vote the most preferred
of the 3 as favourite, and approve all the candidates you prefer to  
the least preferred of  the 3.


What do you think of that?
 



I've had this exact thought... I agree that on paper this should be 
similar in effect and better.
 


Kevin,
Thinking about this a bit more, why not expand this into a fully-fledged 
3-slot method?


Middle-slot votes count only as approval for calculating max. approval 
opposition scores.
Candidates with a Max. AO score greater than 50% of the valid ballots 
are eliminated.

Elect the remaining candidate with most top-slot votes.

I think that would be like a CDTT method. Wouldn't we then have a method 
that meets
Minimal Defense, a variety of Later-no-Harm (middle-rating candidates 
can't harm the voter's top-rated
candidates),FBC and  mono-raise; but fails Plurality,  3-slot Majority 
for Solid Coalitions, and Irrelevant Ballots,

and has a sort of random-fill incentive?

What do you think of that? It seems so Venzke-like, have you ever 
proposed it?


Chris Benham







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Re: [Election-Methods] Mixing Condorcet and Approval...

[Chris Benham]

Elisabeth Varin wrote:

 I read several ways to mix Condorcet and Approval on recent mails.
 This is my favourite, using the latest proposed ballot example.

 I would suggest a Condorcet method usind residual approbation weights
 with an approval cut-off (noted | ).
 It's a mix of Condorcet, IRV and approval.

 The idea is:
 1) to rank candidates using a Condorcet (ranked pairs, winning votes 
 for example) method;
 2) eliminate last candidate like in IRV and give him the weight 
 according to the number of voters
 having that candidate as last approved;
 3) repeat 1) and 2) until winner selection.

Stephane (?),
Am I right in gathering that the approval cutoffs don't actually have 
any effect on who wins??!

Chris Benham




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Re: [Election-Methods] Mixing Condorcet and Approval...

[Chris Benham]

Stephane Rouillon wrote:


I would suggest a Condorcet method usind residual approbation weights
with an approval cut-off (noted | ).
It's a mix of Condorcet, IRV and approval.

The idea is:
1) to rank candidates using a Condorcet (ranked pairs, winning votes
for example) method;
2) eliminate last candidate like in IRV and give him the weight
according to the number of voters
having that candidate as last approved;
3) repeat 1) and 2) until winner selection.

Stephane,
Am I right in gathering that the approval cutoffs don't actually have
any effect on who wins??!

Chris Benham

33: A  B | C
31: B  C | A
33: C | A  B
3:   B | A  C

C is eliminated with 33 votes as support.
B is eliminated with 34 votes as support.
A is last eliminated but receives no rallying voters and finishes with 33
votes as support.

B wins.



Stephane,

I think I now get it, but to say that an  eliminated candidate wins is 
very strange because in the election
method context eliminate normally means disqualify from winning, drop 
from the ballots and henceforth ignore.
From your original description it seemed that the approvals served only 
to give all the candidates each a final approbation

score (just for decoration).

As I now understand it, this method just looks like a very complicated 
way of nearly always electing the Approval winner.


49: A |  C
48: B |  C
03: C |  B

CB 52-48,  CA 52-48,  BA 51-49.  RP(wv) order CBA. 

By my calculation your method elects the Approval winner A, violating 
Majority Loser, Majority for Solid Coalitions and

the Condorcet criterion.

Is that right?

Chris Benham




Yes. Sorry my wife's name comes up when I remote login...
I think your statement is wrong. Let's try a counter-example:

3 candidates A, B, C and 100 voters.
Ballots:
35: A  B  C
33: B  C  A
32: C  A  B

Repetitive Condorcet (Ranked Pairs(winning votes)  ) elimination would produce

at round 1:
68: B  C
67: A  B
Thus ranking A  B  C
C is eliminated.

at round 2:
67: A  B is the ranking
B is eliminated

at round 3:
A wins.

Now in which kind of ballot could an approval cut-off remove some support from
A
and give it to another candidate? Any ballot with A not in first position nor
in last.
Thus concentrating on the C  A  B voters to vote C | A  B instead of C  A
| B
removes final support from A and gives it to C. Not enough A still wins.

Can we obtain an equivalent pairwise succession while raising the number of
adjustable ballots (the ones with A in second position)?
Let's add some B  A  C and try to adapt the others:
33: A  B  C
31: B  C  A
33: C  A  B
3:   B  A  C

Pairwise comparison would produce the same 3 round process (values are
different).
66: A  B
67: B  C
64: C  A

Let's put the cut-offs to disadvantage A:
33: A  B | C
31: B  C | A
33: C | A  B
3:   B | A  C

C is eliminated with 33 votes as support.
B is eliminated with 34 votes as support.
A is last eliminated but receives no rallying voters and finishes with 33
votes as support.

B wins.

This method is proposed within SPPA.

Stéphane Rouillon

Chris Benham a écrit :

 


Elisabeth Varin wrote:

   


I read several ways to mix Condorcet and Approval on recent mails.
This is my favourite, using the latest proposed ballot example.

I would suggest a Condorcet method usind residual approbation weights
with an approval cut-off (noted | ).
It's a mix of Condorcet, IRV and approval.

The idea is:
1) to rank candidates using a Condorcet (ranked pairs, winning votes
for example) method;
2) eliminate last candidate like in IRV and give him the weight
according to the number of voters
having that candidate as last approved;
3) repeat 1) and 2) until winner selection.
 


Stephane (?),
Am I right in gathering that the approval cutoffs don't actually have
any effect on who wins??!

Chris Benham


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Re: [Election-Methods] How does the Schulze Method and Ranking Pairs work?

[Chris Benham]

John,
Have a look at the links.

http://condorcet.org/

http://wiki.electorama.com/wiki/Main_Page

http://wiki.electorama.com/wiki/Smith_set

http://wiki.electorama.com/wiki/Schwartz_set

http://wiki.electorama.com/wiki/Schulze_method

http://wiki.electorama.com/wiki/Ranked_Pairs

http://nodesiege.tripod.com/elections/

Chris Benham


John Wong wrote:

I was wondering, can someone can expliain to me how they how work? 
Also, can someone explain what is the Smith and Schwartz sets are. and 
how do we determine which? Thanks in advance.


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Re: [Election-Methods] How is the Nanson and/or Baldwin non-monotonic?

[Chris Benham]

John Wong wrote:

 How is the Nanson and/or Baldwin non-monotonic? I've been trying to 
 develop an example where they are non-monotonic, but I'm having trouble.


I think this is an example of  Borda Elimination (Baldwin?) failing 
mono-raise.

31: AB
32: BC
03: AC
31: CA
03: CB

Borda scores: C103,  A99,  B98.
Eliminate B, and C wins.

Now change the 3 AC ballots to CA (i.e. do nothing but raise C on some 
ballots without changing any rankings
among other candidates).

31: AB
32: BC
03: CA
31: CA
03: CB

Borda scores: C106,  B98,  A96.
Eliminate A, and B wins.

Note that this doesn't work for (original?) Nanson, because that elects 
C both times (because both times A and B have
below average Borda scores and so are eliminated).

Here is a demonstration from  Douglas Woodall that  that method fails 
mono-raise:

 dabc 40  Borda scores: a 154  average Borda score 150
 bcad 26b 152
 cabd 24c 154
 cdba 10d 140

 With the profile as given, only d is excluded, which results in
 abc 40  Borda scores: a 104  average Borda score 100
 bca 26b 102
 cab 24c  94
 cba 10
 Now c is excluded and a wins.  But if the ten cdba ballots in the
 original profile are replaced by cdab, then the Borda scores become
 a 164, b 142, c 154, d 140, so that b and d are both excluded and c wins.


John Wong wrote:

 How nonmonotonic is Nanson/Baldwin Method? 


John,
The normal meaning of  monotonic is that it meets the mono-raise 
criterion, a binary yes-no test. Woodall has other
monotonicity criteria/properties.  Your question can be interpreted in 
more than one way.

http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf

http://wiki.electorama.com/wiki/Monotonicity_criterion

Chris Benham


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Re: [Election-Methods] How important is the Schwartz criterion? Also, what is the Landau set, and how is different from the

[Chris Benham]

John Wong wrote:

...what is the Landau set, and how is different from the Smith and the 
Schwartz set?



http://lists.electorama.com/mmsearch.cgi/election-methods-electorama.com

http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2000-April/003908.html



  [EM] Landau Winners/Fishburn Set

*Norman Petry [EMAIL PROTECTED] 
mailto:election-methods-list%40eskimo.com

/Sun, 9 Apr 2000 09:58:20 -0600/

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Here is another message from Markus answering some of my questions about
Landau Winners.  This issue arose because Markus included the algorithm
for Landau along with his Schwartz algorithm, and I had some questions about
it.

Again, I thought it might be something of interest to EM generally, so I am
forwarding it to the list for further discussion.

N.

**

Dear Norman,

you wrote (8 Apr 2000):

/ You mentioned the Landau set in your message, but I do not recall that

// Landau has ever been discussed on the EM list.  Does it have any merits or
// uses we should consider?  I did a quick search on the Internet, but turned
// up nothing useful, so if you have any references to Landau I would
// appreciate it.
/
I should have said that the set of Landau winners is called uncovered set
or Fishburn set. If you search for these words, then you will find some
references.

**

A Landau winner is a candidate, who defeats every other candidate with a
path of length 1 or 2.

Candidate A is a Landau winner iff for every other candidate B at least one
of the following two statements is correct:
(1) A = B.
(2) There is a candidate C such that A = C = B.

**

There must always be at least one Landau winner.

**

Miller demonstrated that if (1) the electorate is 2-dimensional, (2) the
voters are sophisticated and (3) the used election method meets the
majority criterion, then the winner must always be a Landau winner.
Therefore, many scholars consider the Landau winners to be the natural
generalization of the Condorcet winner.

[a] Nicholas R. Miller, Graph-Theoretical Approaches to the Theory of
Voting, American Journal of Political Science, vol. 21, p. 769-803, 1977,

[b] Nicholas R. Miller, A New Solution Set for Tournaments and Majority
Voting: Further Graph-Theoretic Approaches to Majority Voting, American
Journal of Political Science, vol. 24, page 68-96, 1980,

[c] Norman J. Schofield, Social Choice and Democracy, Berlin,
Springer-Verlag, 1985,

[d] Philip D. Straffin, Spatial Models of Power and Voting Outcomes,
Applications of Combinatorics and Graph Theory to the Biological and Social
Sciences, edited by Fred S. Roberts, New York-Berlin, Springer, 1989,
page 315-335.

**

I mentioned the Fishburn set only because the calculation of the Fishburn
set is almost identical to the calculation of the Smith set and because
somebody might ask in the future how to calculate the Fishburn set.

**

You wrote (8 Apr 2000):

/ Also, I think your message would be a valuable contribution to the EM list

// archives, for anyone trying to implement Smith, Schwartz, etc.  May I have
// your permission to forward the message to the list?
/
Of course, you may.

Markus Schulze
 






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[Election-Methods] Strong Minimal Defense//FPP (Whole), a new 3-slot FBC method

[Chris Benham]

Kevin, Forest, interested participants,

My latest favourite   FBC single-winner method:

1)Voters submit 3-slot ratings ballot, default 'no rating' interpreted 
as bottom-rating.

2) Eliminate any candidate X  who is above-bottom rated on fewer ballots 
than is some
candidate Y on ballots that bottom-rate X.

3) On ballots that top-rate no candidates, promote middle-rated 
candidates to top- rating.

4) Elect the candidate that is (now) top-rated on the greatest number of 
ballots.

For (at least) the time being, I call this  Strong Minimal 
Defense//FPP(Whole).

It meets a new criterion I suggest that I tentatively label Strong 
Minimal Defense which states:

If  X has fewer votes (ranking/rating above bottom or equal-bottom) in 
total than Y has on ballots
that have no votes for X, then X can't win.

It implies both Minimal Defense and the Plurality Criterion.

The method meets the  FBC  (and therefore the similar Sincere 
Favourite). If  X wins, changing some
ballots that top-rate X and not Y to top-rating both cannot cause X to 
be eliminated or  for any candidate
to be un-eliminated except Y. The changed ballots cannot diminish the 
absolute post-eliminations FPP(W)
score of X and can boost the final score of only Y.

The method compares favourably with the other 3-slot FBC methods. MDDA, 
MAMPO,  MCA, ER-Bucklin (W)
all fail the  Independence from Irrelevant Ballots (IIB) criterion 
which states that if  there is some losing candidate Y
that only appears (voted above bottom or equal-bottom) on some ballots 
that ignore (vote equal-bottom) all other
candidates (and Y is top rated/ranked on fewer ballots than any other 
candidate)  then removing one/some/all of the
Y-plumping ballots must not change the winner

Adding or removing ballots that ignore all the viable candidates can 
change the winner just by changing the size of the
majority threshold. If  the election is contentious and the votes are 
not necessarily counted with the greatest accuracy
and impartiality, it  seems to me to be a great help if election 
monitors/scrutineers/observers can safely pay little attention
to ballots that make no distinction among viable candidates.

SMD//FPP(w)  meets IIB.

I think it meets Majority for Solid Coalitions (aka Mutual Majority) as 
well as any 3-slot method can, meaning that
if more than half the voters rate a subset S of  candidates above all 
others, then a member of  S must win.

In 3-candidate scenarios it generally gives Schulze(winning votes) like 
results.

49: A
24: B
27: CB

A eliminates C because C is above-bottom rated on a total of 27 ballots, 
while on ballots that bottom-rate (ignore) C
A is above-bottom rated on 49 ballots.  Likewise B eliminates A so B wins.

46: AB
44: BC
10: C

C eliminates A, B wins.

46: A
44: BC
10: C

Now C eliminates A, A eliminates  B.   (Like Schulze the method fails 
Later-no-Harm)


40 AB
35 A=B
25 B
  

 From the electowiki  ICA page, giving B as the ICA winner(!?).  

In SMD//FPP(w)  no candidate is eliminated, then A scores 75 versus B's 60.

The method meets mono-raise and fails  Clone-Winner.

I invite comments and am open to suggestions for a more popular name, 
perhaps also for the Strong Minimal Defense
criterion/set.

Links re.  MDDA,  MAMPO, ICA  for comparison :

http://wiki.electorama.com/wiki/Majority_Defeat_Disqualification_Approval

http://wiki.electorama.com/wiki/Majority_Approval%2C_Minimum_Pairwise_Opposition
 


http://wiki.electorama.com/wiki/Improved_Condorcet_Approval

http://nodesiege.tripod.com/elections/#methica


Chris Benham









I

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Re: [Election-Methods] Bullet Voting in the wider media

[Chris Benham]

Abd ul-Rahman Lomax wrote:


If you don't want to use the term sincere here, that's fine by me;
let's use something else. Let's find some term that describes an
ideal method in which a voter can express his true (dictatorial,
perhaps benevolently so, perhaps not) preferences without worrying
that there's some way of voting otherwise to achieve a better result.
   



Well, there is such a method, actually. First of all, you've got to 
collect the necessary data, and the only ballot that does that is a 
Range ballot. But you can analyze a Range ballot as if it were a 
preference ballot with equal ranking allowed. There are two ways to 
go: with sufficient resolution, it can be a simple Range ballot, 
because a voter can maintain a preference of only one rating step, 
which is really pretty small if it is Range 100. It's still pretty 
small with Range 10! However, if the resolution is low, the device 
would be used of having a preference indicator that does not alter 
the Range vote. I.e., you could vote two candidates as perfect 10s 
but still prefer one.


But, it turns out, you would be unlikely to actually do that, in what 
I propose. Basically, the ballots are analyzed two ways: sum of 
votes, which determines a Range nominee, and pairwise. If the Range 
winner is the Condorcet winner, and if the rules allow a victory by a 
plurality (I don't like that), then the election is over. There is no 
question about plurality if the Range winner is preferred by a majority.


But if the Range winner is beaten by another candidate, pairwise by 
preference, then there is a runoff.




Abd,

What do you propose if the Range winner is pairwise beaten by more than 
one candidate?


Chris Benham


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[Election-Methods] IRV variant (was 'Median or ladder voting with candidates')

[Chris Benham]

Kevin Venzke wrote:

Try this method (an IRV variant) for example:

The voter ranks the candidates. Full ranking or
truncation are allowed; equal ranking is not allowed.

Say that X is the number of candidates still in the
running.

While X1:

If more than half of the original count of ballots
rank candidate C in the Xth position (i.e. strictly
last among candidates remaining), then eliminate C.
Otherwise eliminate the candidate with the fewest top
preferences as in IRV.

End while.

Elect the remaining candidate.

Kevin,
It seems to me that the specification of more than
half the original count of ballots instead of more
than half the unexhausted ballots causes this to fail
Independence from Irrelevant Ballots(IIB). What
compensating advantage do you get by doing that?

In the 49A,24B,27CB scenario you have long held that
A shouldn't win because A has the only
majority-strength pairwise loss (to B). And yet no
candidate is ranked strictly last on more than half
the ballots so nothing stops B from being eliminated
and A winning just like in regular IRV.

I suggest this:

Voters rank the candidates,truncation allowed,
above-bottom equal ranking not allowed.

Until one candidate remains, eliminate candidates one
at a time according to these rules:

(1)If one or more of the (remaining) candidates are
not ranked (among remaining candidates)above bottom or
equal-bottom on more than half the ballots that make
some ranking distinction among remaining candidates,
eliminate the one of these that is top-ranked (among
remaining candidates) on the fewest ballots.

(2)Otherwise eliminate the candidate that is
top-ranked (among remaining candidates) on the fewest
ballots.

Elect the remaining candidate.

What do you think of that? This meets Sincere Defense
and keeps IRV's IIB while being much more Condorcetish
than regular IRV.

Chris Benham
 



Thu Dec 20 21:43:33 PST 2007 

Hi,

I think an approach towards implementing this kind of
logic in an election with unnumbered candidates would
be to allow voters to torpedo the options they
perceive as furthest from them.

Try this method (an IRV variant) for example:

The voter ranks the candidates. Full ranking or
truncation are allowed; equal ranking is not allowed.

Say that X is the number of candidates still in the
running.

While X1:

If more than half of the original count of ballots
rank candidate C in the Xth position (i.e. strictly
last among candidates remaining), then eliminate C.
Otherwise eliminate the candidate with the fewest top
preferences as in IRV.

End while.

Elect the remaining candidate.


Imagine that the candidates can more or less be
plotted on a one-dimensional spectrum. Considering
that candidates are more likely to try to stand as
near to the median as possible, and not spread
throughout the space where voters lie, IRV is likely
to eliminate all the median options and end with a
final showdown between two strong candidates who
were able to grab large quantities of outer voters.

In this variant method, assuming these two candidates
aren't the preference of the median voter, it is
likely that IRV's two finishers could be the
first two candidates eliminated. Their supporters'
second preferences would very quickly be freed up to
help support candidates closer to the median.
And this process is capable of repeating indefinitely
until the final two candidates are truly those that
came nearest to the median.


This is an instant generalization of my two-round
method suggestion where the final round consists of
the top two candidates from the first round,who didn't
receive a full majority of the against votes of that
round.

Kevin Venzke






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[Election-Methods] IRV ballot is at least as fair as FPTP ballot

[Chris Benham]

Kathy Dopp wrote:
Wed Dec 26 15:41:47 PST 2007 

One problem is that my second choice candidate may be
eliminated in the first round and my first choice
candidate not have success either - despite the fact
that my second choice candidate is the most popular
among all voters.

For instance, this example, which is one of countably
infinite examples where IRV elects the candidate not
supported by most voters:

Republican  Libertarian Progressive Democrat
1st choice  4   3   3   2
2nd choice  1   2   1   7
3rd choice  1   1   6   1


I.e. in this example with 12 voters, the Democrat
loses in the first round, even though the most number
of persons supported the Democrat overall - letting
the Republican win, even though the Republican (in
this example) is not as widely supported as to other 
candidates.

Kathy,
I would find your example much more comprehensible and
interesting if it was presented as an election
profile showing the voters' rankings, such as:

49:A
24:B
27:CB

In your example it is quite possible that the
Republican is the sincere ratings winner, and also a
point scoring method such as you advocate could elect
the Republican if the arbitrary point schedule scores
first choices much higher than second and third
choices.

What point schedule appeals to you, and how do you
suggest truncation be handled?

Do you support Approval?

Chris Benham







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[Election-Methods] Strong Minimal Defense//FPP (Whole), a new 3-slot FBC method

[Chris Benham]

Hello participants,
I no longer advocate what I had touted as my latest
favourite FBC method because Kevin Venzke pointed out
how it could fail FBC, prompting me to compose this
example:

10:AC
09:B
03:C
10:D
02:D=B (or DB or BD, sincere is BD)

In SMD//FPP(W), using the Strong Minimal Defense
device B eliminates A and then C wins. But if the 2D=B
voters had instead voted D (meaning DB=C) then no
candidate would be eliminated by SMD and so D would
win.

Thanks Kevin. I'm still interested in 3-slot methods
that meet FBC or 3-slot Condorcet and will probably
post a (hopefully) better method suggestion soon.

Chris Benham 


http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2007-September/020863.html
Sun Sep 23 12:30:45 PDT 2007 

Kevin, Forest, interested participants,

My latest favourite   FBC single-winner method:

1)Voters submit 3-slot ratings ballot, default 'no
rating' interpreted as bottom-rating.

2) Eliminate any candidate X  who is above-bottom
rated on fewer ballots than is some candidate Y on
ballots that bottom-rate X.

3) On ballots that top-rate no candidates, promote
middle-rated candidates to top- rating.

4) Elect the candidate that is (now) top-rated on the
greatest number of ballots.

For (at least) the time being, I call this  Strong
Minimal Defense//FPP(Whole).

It meets a new criterion I suggest that I tentatively
label Strong Minimal Defense which states:

If  X has fewer votes (ranking/rating above bottom or
equal-bottom) in total than Y has on ballots that have
no votes for X, then X can't win.

It implies both Minimal Defense and the Plurality
Criterion.

cut




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Re: [Election-Methods] RE : Taiwan legislative elections and referendum

[Chris Benham]

Kevin Venzke wrote:


Hi,

--- Augustin [EMAIL PROTECTED] a écrit :
 

I am very angry when I think about how referendums are conducted in 
Taiwan. 


a- stupid 50% rule.
---

For the result of a referendum to be valid, at least 50% of the 
*registered voters* must participate. I.e. if at least 50% of the 
registered couch potatoes stay at home, the referendum will fail even 
if the vote expressed show 90% +  support to the referendum item.


Thus, the surest way to kill a referendum is to stay at home.
Also, all those registered voters who genuinely don't care about the 
referendum one way of the other (e.g. the disinterested couch potato 
group of people), are all automaticall counted in the NO camp, 
whatever the question asked. !!!


How much more undemocratic can that be??
   



The rule that a majority of voters must vote is unfortunate because it
means that by showing up to vote No you can cause the proposal to
succeed.

You could  avoid that problem by having a rule that says for a 
referendum to pass the number of
cast ballots in favour of it must exceed the number of  cast ballots 
against it and also comprise at
least (say) 25%  of  the registered voters.  (The 25% figure is 
consistent with the intention of the
actual 50% must vote rule, because if it passes by a narrow margin 
then about 50% must have

voted.)

I think a rule like this is more democratic than having super-majority 
requirements that exist in a lot

of places.


But in my opinion, to avoid government abuse of referendum, they should not
pass or fail only on the opinions of the voters that the government was
able to convince to participate.
 

Kevin, can you explain (and maybe give an example) of what you mean by  
government abuse of referendum

and how your proposal avoids it?


If I choose to not vote in a referendum for some issue, I want this to be
interpreted as have the government make this decision not let the other
voters make this decision.

Since the government derives its authority and legitimacy from being the 
voters' representatives, I find
this personal view of  yours to be a bit perverse and undemocratic. 
Presumably you think this should

be the general view. If so, why?


Chris Benham




 


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[Election-Methods] [Election Methhods] MCA's IIB problem fixed

[Chris Benham]

Kevin,
In your latest post  you alluded to  MCA's failure of  Independence from 
Irrelevant Ballots (IIB):

A nice thing about the majority requirement is that if it's assumed that
you are going to vote, there's no way that your vote can move the majority
from one candidate to another.

But but the bad thing about the majority requirement is that  choosing 
between not voting and voting
for nobody (ignoring the competitive/viable candidates) can change the 
winner by changing the majority
threshold.

I suggest that MCA instead of  electing the top-ratings winner only if  
that candidate's top-ratings score
is greater than half the total number of valid ballots, it elects the 
top-ratings winner (TRW)  if  the TRW's
top-ratings score is not smaller than his/her maximum pairwise opposition.

(Here I'm referring to the FBC complying version of  MCA that uses 
3-slot ratings ballots, but this
mechanism could equally be used for the version you were discussing that 
uses hybrid FPP-approval
ballots, and also to Bucklin.)

Doesn't this fix MCA's  IIB problem at no cost (except a bit more 
complexity)?


Chris  Benham



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Re: [Election-Methods] MCA's IIB problem fixed

[Chris Benham]

Kevin,
I just realised that my suggested IIB-fix of  MCA  does cost a criterion 
compliance:
Later-no-Help.  Adding  middle-ratings can help top-rated candidates by 
maybe

increasing the Max Pairwise Opposition of  their rivals.

I consider having LNHelp and  LNHarm in  (at least probabilistic) 
balance to be more
desirable than either by itself,  so  I  don't mind losing  MCA's  
LNHelp  (since it badly
fails LNHarm).  But  I have to withdraw my suggestion that  MCA doesn't 
have (for a

3-slot method) a maximal set of properties.

And  I  think there are better 3-slot  FBC-complying,  LNHelp failing 
methods that use
MPO information combined with ratings information (than my suggested 
modified MCA).


One possibility:  If  any candidates have a top-ratings score not 
smaller than their  MPO
score, disqualify the other candidates.  Elect the undisqualified 
candidate with the highest

Approval minus MPO score.


Chris  Benham




Kevin Venzke wrote:


Chris,

--- Kevin Venzke [EMAIL PROTECTED] a écrit :
 


Kevin,

Kevin Venzke wrote:

As far as my strategy simulation is concerned, this rule change raises
the
question of how voters should evaluate the possibility that they elevate
a
candidate to the top spot on first preferences only to see him lose due
to
pairwise opposition.

   


Chris replies:
 


I don't fully understand this point.  Any candidate who would win in the
first round of regular  MCA would 
also win in the first round of  my suggested version, and in both the FPW

can win in the second round.
The only difference is that my version is more likely to have a
first-round winner, which I suppose in the
FBC-complying 3-slot ballot version might be a bit self-defeating.  In
your  FPP-approval ballot version
I don't see how it greatly complicates the strategy.
   



Currently the value of a first-preference vote for A is estimated as the
likelihood that A can achieve majority times the likelihood that no
candidate will achieve majority (e.g. if a majority is guaranteed then no
vote is of value) times the difference between A's utility and your
expectation should the election be resolved on approval.

With your rule you no longer simply break ties between one candidate's
majority and no majority; you have to compare against each other
candidate FPP-style. And you can't simply compare the candidate's utility
to the approval expectation, because the candidate could lose despite
coming in first.

If I were implementing this method I would probably have voters keep track
of their expectation when each candidate is the TRW but has too high
pairwise opposition. This kind of approach so far has produced a lot of
intelligent behavior. It has a couple of downsides though: 1. Voters can't
predict the value of situations which weren't observed to occur in the
polls, and thus won't try to create them, and 2. There seem to be a number
of cum hoc ergo propter hoc mistakes where voters vote for situations
that have coincided with outcomes they liked, but which didn't necessarily
cause them.

Kevin Venzke


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Re: [Election-Methods] Fwd: [Election Methhods] MCA's IIB problem fixed

[Chris Benham]

Kevin,

Kevin Venzke wrote:


I also don't find the FBC-satisfying version of MCA to be a
significant improvement over Approval.



I like it better than  3-slot CR.  I agree that in scenarios where it is 
known to be very likely
no majority first-round winner then it is just  Approval with extra 
voter expression and when
it is considered possible that there will be a first-round winner then 
that prophesy will quickly tend
to become self-fulfilling and the method tends to become Approval with 
a silly ballot option

(the middle slot) for strategic mugs.

In principle I don't like restricted ranking ballots or hybrid 
ballot-types with a restricted ranking

component.


As far as my strategy simulation is concerned, this rule change raises the
question of how voters should evaluate the possibility that they elevate a
candidate to the top spot on first preferences only to see him lose due to
pairwise opposition.

I don't fully understand this point.  Any candidate who would win in the 
first round of regular  MCA would
also win in the first round of  my suggested version, and in both the 
FPW  can win in the second round.
The only difference is that my version is more likely to have a 
first-round winner, which I suppose in the
FBC-complying 3-slot ballot version might be a bit self-defeating.  In 
your  FPP-approval ballot version

I don't see how it greatly complicates the strategy.


Well, if you're considering using MCA then you probably care about
complexity. 

I used to think that for a 3-slot method it had a  maximal set of 
properties  (though not necessarily

the most attractive set)  and that the great simplicity  was a bonus.


Chris Benham



Chris,

--- Chris Benham [EMAIL PROTECTED] a écrit :
 


Kevin,
In your latest post  you alluded to  MCA's failure of  Independence from 
Irrelevant Ballots (IIB):


   


A nice thing about the majority requirement is that if it's assumed that
you are going to vote, there's no way that your vote can move the
 


majority

from one candidate to another.
   

But but the bad thing about the majority requirement is that  choosing 
between not voting and voting
for nobody (ignoring the competitive/viable candidates) can change the 
winner by changing the majority

threshold.

I suggest that MCA instead of  electing the top-ratings winner only if  
that candidate's top-ratings score
is greater than half the total number of valid ballots, it elects the 
top-ratings winner (TRW)  if  the TRW's

top-ratings score is not smaller than his/her maximum pairwise
opposition.

(Here I'm referring to the FBC complying version of  MCA that uses 
3-slot ratings ballots, but this
mechanism could equally be used for the version you were discussing that 
uses hybrid FPP-approval

ballots, and also to Bucklin.)

Doesn't this fix MCA's  IIB problem at no cost (except a bit more 
complexity)?
   



Well, if you're considering using MCA then you probably care about
complexity. I also don't find the FBC-satisfying version of MCA to be a
significant improvement over Approval.

In terms of criteria, at first glance it seems like this has a good chance
of preserving FBC since pairwise opposition is friendly to it. I'm not
totally sure.

As far as my strategy simulation is concerned, this rule change raises the
question of how voters should evaluate the possibility that they elevate a
candidate to the top spot on first preferences only to see him lose due to
pairwise opposition.

Kevin Venzke


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[Election-Methods] MCA's IIB problem fixed

[Chris Benham]

Hello,
I've been thinking about 3-slot methods that combine
Top Ratings, Approval and Pairwise Opposition
information (all concepts that are compatible with FBC
and Independence from Irrelevant Ballots) to produce a
method that meets those criteria and also 3-slot
Majority for Solid Coalitions and mono-raise and also
which has its LNHarm and LNHelp problems in
approximate balance.

In my last message in this thread I suggested one
possibility to be:

If  any candidates have a top-ratings score not
smaller than their  MPO score, disqualify the other
candidates.  Elect the undisqualified candidate with
the highest Approval-minus-MPO score.

This has now firmed as my preferred 3-slot (FBC
complying) method.

Any comments?  I have no idea what it should be
called.

Chris Benham




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[Election-Methods] A better IRV (was Re: Range Voting won't eliminate spoilers)

[Chris Benham]

Steve Eppley wrote:
IRV might cause polarization even worse than what we already have, since 
the effective plurality rule campaign strategy of shifting toward the 
centrist swing voters after being nominated--which reduces polarization 
somewhat--would risk, under IRV, the late entry of an independent 
candidate competing at a position slightly closer to the party base.

Some people might think that (for many elections) providing voters with extra
meaningful choices is more important than  reducing polarisation.


IRV can be significantly improved by letting candidates withdraw from 
contention after the votes are cast.

That is debatable. This seems to be based on the assumption that IRV is a
lousy method because it fails Condorcet and Minimal Defense and when on 
the sincere preferences there is a Condorcet winner who is not a Dominant
Mutual Third (DMT) winner then some of the voters have incentive to use the 
Compromise strategy; and so that any modification that reduces these 
problems must be a big unambiguous improvement.

On the other hand I consider that it is one of the good methods because it has
some redeeming positive properties that are incompatible with those that it 
lacks.

One of its good properties (criterion compliances) that endears it to its 
supporters
is that it meets Later-no-Harm.  IRV improved in the way Steve suggests 
doesn't.

49: A
24: B (sincere is BC)
27: CB

Normal IRV elects A. The voters have no incentive to truncate, including the 24 
B
voters who could have created a preferable result for themselves (the election 
of C)
by voting their full sincere rankings.

But with Steve's suggested option of allowing candidates to withdraw after the 
ballots
have been cast and analysed, the B supporters' truncation can pay off  if  C 
plays the
game and withdraws. If they don't insincerely truncate then B can't win (unless 
C is 
somehow induced to withdraw from an unassailable win), so that is a failure of  
Later-no-Harm.

As I made clear in a previous post, I am philosophically opposed to to having 
the results 
of elections determined by the machinations and manoeuvres of  
candidates/parties 
*after* the voters have cast their ballots.

Chris Benham



Steve Eppley wrote Mon Mar 17  2008:

...However, IRV is worse at eliminating spoilers than some other methods.  
It also undermines candidates who take centrist compromise positions, by 
defeating them and making them appear unpopular.  As a consequence, we 
can expect IRV would continue the two big polarized parties, each 
nominating one candidate per office system (including its haphazard 
primary elections).

IRV might cause polarization even worse than what we already have, since 
the effective plurality rule campaign strategy of shifting toward the 
centrist swing voters after being nominated--which reduces polarization 
somewhat--would risk, under IRV, the late entry of an independent 
candidate competing at a position slightly closer to the party base.

IRV can be significantly improved by letting candidates withdraw from 
contention after the votes are cast.  At the end of election day, the 
votes would be published in a format that candidates (and others) can 
download.  Then the candidates would be given a few days to decide 
whether to withdraw.  They could use those days to calculate what the 
result would be with or without themselves (and/or some other 
candidates) in the voters' rankings, and to negotiate with supporters 
and with other candidates about who, if anyone, should withdraw.  The 
official winner would not be tallied until after the withdrawal period.

--Steve


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[Election-Methods] Cumulative Approval

[Chris Benham]

Juho wrote:
I presented only some positive examples. Also various bad failure  
cases would be appreciated if you can find good examples.

Juho,

31: AB
32: BC
37: C

C is clearly the strongest candidate, having both more first preferences
and more second preferences than either of the other candidates.

Your suggested Cumulative Approval method elects B.

Unlike  IRV or  Bucklin, your suggested method fails Later-no-Help.

31: AB
32: BC
37: CA

The C voters have added a second preference for A, which causes
the winner to change from B to C.

Like  IRV it fails Mono-raise and so is vulnerable to the Pushover
strategy.

49: A
27: BA
24: CB

Your suggested method elects B.


45: A
04: CA  (was A)
27: BA
24: CB

Now your method elects A.

Of course it fails Later-no-Harm.

49: A
24: B
27: CB

B wins, but if  the B voters change to BC then C wins.

The method fails Kevin Venke's Sincere Favourite (and therfore
fails FBC).
http://nodesiege.tripod.com/elections/#critsf

31: A=B
32: BC
37: CA

The method elects C.

31: BA  (was B=A)
32: BC
37: CA

Now  it elects B. Some voters have changed the winner from not 
one of their most preferred to one of their most preferred by dropping
one of their most preferred from the top-most ranking (or rating) on
their ballots.  This is a failure of  Sincere Favourite.


Chris Benham







Juho juho4880 at yahoo.co.uk 
Thu Apr 3 13:57:22 PDT 2008 

Here's one new method (as far as I know, tell if you have seen this  
before) for your consideration.

One viewpoint to this method is that it tries to make the sequential  
process of IRV better than what it is in the basic IRV. On the other  
hand this can be seen also as an Approval method where the approval  
cutoff can move.

The voters will rank the candidates (equal rankings are ok). The vote  
counting algorithm is based on collecting cumulatively approvals for  
the candidates.

The algorithm follows roughly the following philosophy.

(a) tentatively elect a winner
(b) voters are given the chance to compromise and approve more  
candidates to find a better winner (approvals are final and can not  
be canceled)
(c) those voters whose so far approved candidates are weakest at one  
moment shall compromise first

I explained this rough philosophy before the algorithms since this  
hopefully helps when going through the detailed descriptions below.

First one rather complex procedural description of the method.

(1) all voters approve their favourite candidate(s)
(2) find those candidates that have most approvals (=leaders) (also  
partial tie breaking possible here)
(3) find those voters that have not yet approved all the leaders
(4) take from that set only those voters who still have not approved  
all the candidates that they prefer to the least preferred leader(s)
(5) take from that set only those voters who approve the lowest  
number of the leaders
(6) take from that set only those voters whose best approval result  
among the approved candidates is lowest
(7) these voters will change their vote to approve also the next  
candidate(s) (in their order of preference)
(8) if there were still such voters jump back to point (2)
(9) elect the candidate with highest number of approvals (use tie  
breaker if needed)

This description was quite complex because of the all tie related  
concerns. The following version of the algorithm is a bit simpler. It  
breaks all ties in the results as soon as they are encountered  
(unlike the algorithm above that allowed multiple leaders to exist).  
In large public elections both approaches typically yield the same  
results since ties are very rare in large elections. Rows from (2) to  
(5) have been modified.

(1) all voters approve their favourite candidate(s)
(2) find the candidate that has most approvals (leader) (use tie  
breaker if needed)
(3) find those voters that have not yet approved the leader
(4) take from that set only those voters who still have not approved  
all the candidates that they prefer to the leader
(5)
(6) take from that set only those voters whose best approval result  
among the approved candidates is lowest
(7) these voters will change their vote to approve also the next  
candidate(s) (in their order of preference)
(8) if there were still such voters jump back to point (2)
(9) elect the candidate with highest number of approvals (use tie  
breaker if needed)

In all tie breaking cases above the simplest tie breaker is basic  
lottery, but also other additional criteria could be used.

Here's one example calculation (a typical simplified left-centre- 
right example).

Votes:
49: ABC
12: BAC
12: BCA
27: CBA

- first all approve their favourites

49: ABC
12: BAC
12: BCA
27: CBA

- A is the leader
- BCA and CBA voters could compromise
- BCA voters will compromise since B has only 24 approvals (C has 27)

49: ABC
12: BAC
12: BCA
27: CBA

- A is still the leader
- now the CBA voters must compromise

49: ABC
12: BAC
12: BCA
27: CBA

- B is the leader
- all voters have

[Election-Methods] Clone-related problems (was Re: Clone related problems in Range/Approval)

[Chris Benham]

Steve Eppley SEppley at alumni.caltech.edu 
Sat Apr 19 08:49:43 PDT 2008 
I agree with Mr. Lomax that parties' main purpose is to coordinate 
campaigns, if he means coordinating the *votes* by assembling a 
coalition large enough either to win or to elect a lesser evil 
compromise that defeats a greater evil.  Given traditional plurality 
rule or top two runoff or Instant Runoff or many other methods, parties 
fail to coordinate a large enough coalition if they nominate more than 
one candidate per office. 
Steve,
Since IRV  meets Clone-Winner I don't see how your claim applies to it.
While of course a party that endorses say two candidates A and B could
lose because some of its supporters didn't rank both A and B above all
the other candidates, I am sure that with voluntary voting in general that
negative would be overwhelmed by the effect of attracting more of their
supporters to vote.
It could be the case that one or both of  A and B are resolved to run with
or without their party's endorsement, so endorsing both might make for
a tighter exchange of preferences.

Voting for a Published Ranking
    Prior to election day, each candidate publishes a ranking
    of the candidates.  On election day, each voter selects one
    candidate. (What could be simpler?)  Each vote is replaced
    by the ranking published by the voter's selected candidate.

Assume for this discussion that the algorithm VPR uses to tally the 
rankings doesn't suffer from Borda's awful inferior clones problem and 
that one of the following conditions is true:

    1. The algorithm elects within the top cycle.

    2. The votes are published, then each candidate may choose to
    withdraw from all the rankings before the rankings are tallied.
    (Candidates can withdraw to elect a compromise and defeat
    a greater evil.)
So you want to constrain voters to only vote one of the rankings decided
by the candidates (or their backers in their name), thus in effect making
the candidates privileged super-voters; and on top of that you want to
give candidates the power to manipulate the result by withdrawing 
after the votes have been cast?
I would expect any voter with any concept of voter sovereignty and who isn't
a dumb sheep to object to that.

In a previous post I pointed out that allowing candidates to withdraw after
the votes have been cast (and counted) creates big incentives for corruption.
Constraining voters to only vote their favourite's published ranking makes it
much easier for the candidates/parties to make and deliver on preference
swap deals that might be completely unprincipled, opportunistic and 
ideologically
incongruous. It would also bizarrely magnify the clout of  very minor candidates
because of their total control over their supporters' full voted rankings.

Something like Forest Simmon's DYN method is far less objectionable, because
the voters have to opt in to having their vote in part commandeered by one of 
the
candidates. If  they ignore that option then it is just an Approval election.

Chris Benham


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[Election-Methods] [Election Methods] Re: 3-slot ICA fixed to meet 2-candidate Condorcet?

[Chris Benham]

Maybe more exact is:

3-slot ballots, default rating Bottom, Top and Middle interpreted as
approval. 

If any there are any candidates whose Top ratings score is higher than his 
or her maximum pairwise opposition score, elect the one of these with the
highest TR score.

Otherwise elect the regular ICA winner.


Chris Benham



Chris Benham wrote (Apr.28):

Kevin,
Your  Improved Condorcet//Approval (ICA) method I take attempts
to minimally modify Condorcet//Approval(ranking) so that it meets
Sincere Favourite (your version of  FBC).


http://nodesiege.tripod.com/elections/#methica


http://nodesiege.tripod.com/elections/#critsf


48: AB
02: B
49: B=A
01: C

AB 48-2,  AC 97-1.

In this virtual 2-candidate election, ICA elects B.

To fix this, I suggest: 

3-slot ballots, default rating Bottom, Top and Middle interpreted as
approval. 

If the Top ratings winner T has a TR score higher than T's
maximum pairwise opposition score then elect T.

Otherwise elect the regular ICA winner.


This seems to be a pure improvement. What do you think?


Chris  Benham


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Re: [Election-Methods] IRV ballot is at least as fair as FPTP ballot

[Chris Benham]

Kathy Dopp wrote:

Kathy Dopp kathy.dopp at gmail.com 
Sat May 3 21:29:19 PDT 2008 

..However, even despite some voters using strategy because they realize
that IRV fundamentally does not work the way it is intended to, you
will undoubtedly find ample number of cases of candidates winning
elections who were not preferred by most voters. ..


Kathy,
In a previous post I  nit-picked an anti-IRV example you gave. Yes, it is
possible for  IRV to elect a candidate that is apparently not the
strongest.
31: AB
32: BC
37: C
http://lists.electorama.com/pipermail/election-methods-electorama.com/2007-December/021192.html

What exactly does your phrase not preferred by most voters mean (or refer to)?
Does it just refer to  IRV's failure of the Condorcet criterion?
The  Alternative Vote  (voters strictly rank from the top however many or few 
candidates they wish,
until one remains eliminate the  remaining candidate that is top ranked among 
remaining candidates on 
the fewest ballots) has a maximal set of positive properties. 

Therefore to credibly attack  (this version of) IRV, you might like to tell us 
which of  it's positive 
properties you think  are less valuable than ones you prefer and maybe give an 
example of  a
precisely defined method that you claim is better.


Chris Benham


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[Election-Methods] [Election Methods] Bucklin-like method suggestion (following from MCA's IIB problem fixed)

[Chris Benham]

Kevin (and interested others),
I'm interested in reaction to this suggestion for a method:
Voters fill out ratings ballots with 4 or more fixed slots (or maybe
with the number of slots being the number of candidates plus 1 or 2).
(1) If the candidate T that is top-rated on the most ballots has a top-ratings
(TR) score higher than T's maximum pairwise oppostion (PO) score,
then elect T.
(2) If  not, promote on all ballots any candidates in  the next-lowest rating
slot to Top and recalculate TR and PO scores accordingly.
(3) Repeat steps (1) and (2) until there is a winner.  End.

This is an extension to 4 or more slots of  my Jan.2008 idea for modifying
Majority Choice Approval (MCA), which uses a 3-slot ratings ballot.
The idea is to keep the Bucklin virtues of  meeting Majority for Solid 
Coalitions,
Favourite Betrayal (and Sincere Favourite) and Minimal Defense and Plurality
(and my suggested Strong Minimal Defense)*, while trading away Later-no-Help
for Independence from Irrelevant Ballots (IIB).
As you know I think it is better that LNHarm and LNHelp be in approximate
probabilistic ballance rather than there be either strong incentive to truncate 
or
a random-fill incentive, so therefore I regard the trade-off I referred to as 
really
a win-win.
Chris Benham

* Strong Minimal Defense: if more voters vote for (meaning rank or rate above
bottom)  X and not Y than vote for Y, then Y can't win.


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Re: [Election-Methods] I Need Reviews of Ten Reasons to Oppose IRV

[Chris Benham]

Kathy Dopp has persisted in producing a paper on IRV. She concludes:

Ranked choice (RCV) / instant runoff voting (IRV) is not worthy of 
consideration and its use should be avoided.

Chris Benham
The eight page report 15 Flaws and 3 Benefits of Instant Runoff or
Ranked Choice Voting explains the flaws and benefits of instant
runoff voting in detail plus provides appendices with examples of how
RCV/IRV violates fairness principles, plus provides three pages of
endnotes of references and additional facts.

The full report is available on-line at
http://electionarchive.org/ucvAnalysis/US/RCV-IRV/InstantRunoffVotingFlaws.pdf

This release is also posted online at
http://electionarchive.org/ucvAnalysis/US/RCV-IRV/FlawsIRV-PressRelease.pdf
or at http://kathydopp.com/serendipity/



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Re: [Election-Methods] Reducing 3-cand elections to 8 scenarios

[Chris Benham]

A couple of drastic measures that appeal to me are only accepting (and 
requiring) a first and a second preference, 
and to the extent necessary, discarding ballots that won't cooperate in voting 
for the top three candidates (according 
to first preferences).

Kevin,
I have the same question I had the last time you proposed a method focused on 3 
candidates:
Instead of  discarding ballots, why not apply these methods to the ballots 
modified by eliminations
after all but 3 candidates have been IRV-style one-at-a-time eliminated?
Another measure occurred to me: Among the supporters of each of the top three 
candidates, play winner takes all 
for the second preference. In other words, all of the second preferences from 
the A-first voters are considered to 
be cast for whichever (of the other two candidates B and C) received more. This 
has a consequence that not giving 
a second preference (if such were allowed) is never optimal; your second 
preference is just determined by other voters 
with the same first preference.
With this weird  (but I suppose not in principle unacceptable) feature, what is 
the point of  requiring a second preference?
Chris Benham





[Election-Methods] Reducing 3-cand elections to 8 scenarios
Kevin Venzke stepjak at yahoo.fr 
Sat Jun 14 10:02:33 PDT 2008 


Hello,

Lately I've been thinking again about how to adjust a method's incentives in 
order to encourage a state of affairs 
where there are three competitive candidates, each of whose strategy is to 
stand near the median voter.

A couple of drastic measures that appeal to me are only accepting (and 
requiring) a first and a second preference, 
and to the extent necessary, discarding ballots that won't cooperate in voting 
for the top three candidates (according 
to first preferences).

Another measure occurred to me: Among the supporters of each of the top three 
candidates, play winner takes all 
for the second preference. In other words, all of the second preferences from 
the A-first voters are considered to 
be cast for whichever (of the other two candidates B and C) received more. This 
has a consequence that not giving 
a second preference (if such were allowed) is never optimal; your second 
preference is just determined by other voters 
with the same first preference.

When we play winner takes all in this way, there are only 6 possible ballot 
types, only 3 of which can occur in the same 
election, and there are only 8 possible elections.

This makes it very easy to describe many methods and then compare their 
strategic vulnerabilities. First, say that the 
candidates A B and C name the three candidates in decreasing order of 
first-preference count. Also, assume that all 
methods will elect a majority favorite, so that in all 8 scenarios, we know 
that any two factions are larger than the third.

Here is how I've ordered the scenarios:
The two cycles:
1 ab bc ca
2 ac ba cb
The six with majority coalitions:
3 ab ba ca
4 ab ba cb
5 ab bc cb
6 ac bc cb
7 ac ba ca
8 ac bc ca

I can define methods by which candidate wins in each scenario:

FPP:
AA AA
IRV:
AB ABBBAA
DSC and (my method) SPST:
AA AABCAA
VFA:
AA AABBAA
Schulze, MMPO, etc.:
AA ABBCAC
Bucklin, MF/Antiplurality:
BA ABBCAC
IRV/DSC combo:
AB ABBCAA

The last method takes the DSC result for scen 6 but otherwise uses the IRV 
result.

For each method I can mostly summarize the rule:
FPP: Elect A.
IRV: Elect C faction's second preference.
DSC: If there's a majority coalition excluding A, elect A faction's second 
preference; else elect A.
VFA: If there's a majority coalition excluding A, elect B; else elect A.
Schulze: If a candidate has no last preferences, elect that one; else elect A.
Bucklin: If a candidate has no last preferences, elect that one; else elect C 
faction's last preference.
IRV/DSC combo: If there's a majority coalition excluding A, elect A faction's 
second preference; else elect 
C faction's second preference.

I evaluated two types of strategies from each faction's perspective:
Compromise: The faction tries to improve the result by swapping their first and 
second preferences, creating 
a majority favorite (autowinner).
Burial: The faction tries to improve the result by swapping their second and 
third preferences.

I have a lot of scratchpaper for this task, but I think I'll just show the 
results.

For each method, the scenarios go across as they do above. The values in a 
position can be yes, the strategy 
helped; no the strategy did nothing; and worse as in, the strategy made the 
outcome worse.

Unintuitively the six rows are in this order:
Compromise by C faction
Compromise by B faction
Compromise by A faction
Burial by A faction
Burial by B faction
Burial by C faction

FPP
ny nyyynn
yn nnyyny
ww ww
nn nn
nn nn
nn nn

FPP has no burial strategy, but a lot of potential for compromise strategy by B 
and C factions. No strategy for A faction.
# of stable scenarios: 2
y vs w count: 8 to 8

IRV
nn nn
yw nwwwny
wy

Re: [Election-Methods] RELEASE: Instant Runoff Voting (Chris Benham)

[Chris Benham]

Kathy,
I choose my words carefully. 

You managed to invent a really bad voting method (asking voters for
ratings and then converting their ratings to approval/disapproval by
your new voting method) and applied your method of conversions to your
own example, but it has nothing to do with either range or approval
voting methods.


Apart from a passing reference to Range the only voting method I discussed
or referred to was Approval. 
I didn't suggest that voters be asked for ratings.
40: A100, B98
25: A98,   B1
35: B100, A1
These numbers I gave  represent nothing outside the heads of the individual 
voters.
I'm sorry if I didn't make that clear enough.  This corresponds with the use in 
EM circles of the word  utilities.

Chris  Benham



Kathy Dopp kathy.dopp at gmail.com 
Sat Jun 21 17:54:52 PDT 2008 
Chris,

You example clearly does not provide an example of approval voting
being subjected to the spoiler effect.

You managed to invent a really bad voting method (asking voters for
ratings and then converting their ratings to approval/disapproval by
your new voting method) and applied your method of conversions to your
own example, but it has nothing to do with either range or approval
voting methods.

Chris, This is the LAST time I will take any of my time to respond to
any of your emails since your emails either lack any logic or show
that you did not take the time to read and study either Abd ul's email
rebuttals of Fair Vote or the paper I wrote and I don't have time to
waste on annoying silliness.

On Sat, Jun 21, 2008 at 5:03 PM,   Date: Sat, 21 Jun 2008  Ok.
Suppose the method is Approval, there are two candidates (A and B)
and the voters'
utilities (sincere ratings on some fixed scale independent of the candidates) 
are:
40: A100, B98
25: A98, B1
35: B100, A1

OK. Then if this example is counted using approval voting by removing
the ratings for these voters, there is a TIE since 100% of voters
approve of both A and B.


I assume that with just 2 candidates, all voters will simply approve the one 
they prefer to
the other, to give the Approval result:
65: A
35: B

OK. This is a completely separate example of approval voting than your
first example.  BTW, in any election:

1.  voters have to make a choice on how they vote and cannot vote more
than one way in the same election using one ballot, and

2. the election has to be either conducted via one election method or
another - I.e. approval voting is analogous to rating candidates 0
(not approved) or 1 (approved), and so your above example shows ALL
candidates are approved if one tries to switch that to approval from
ratings.

In this example A wins.

A wins. Now suppose that a third candidate (C) is introduced, and including 
this extra
candidate the voters' utilities are:


40: A100, B98, C1
25: C100, A98,B1
35: B100, C98, A1

OK. In this example, removing the ratings to get approval voting
example (a third example related to neither of the first two, ALL
voters approve of A, B, and C and so A, B, and C are TIED again. It
seems like a pretty unlikely scenario, but then I suppose it is
possible.

Now all the voters have one candidate they like very much, another they like 
nearly as much,
and one they like very much less. The voters best zero-information strategy is 
to all approve 2
candidates, to give the Approval ballots:
40: AB
25: CA
35: BC

OK, in THIS (yet another separate example of approval voting which is
not related to either of your prior examples in any way except by
dropping particular candidates from prior examples), B wins.

You are capable of understanding I hope that this example is entirely
different from your prior examples and that none of your examples are
of the same approval election?

If you are illogically claiming that these three entirely separate
examples are the same you must (I am guessing) be thinking in
backwards fashion that you can devine voter ratings from approval
ballots or that you can delusionally know how all voters would change
ratings to approval votes and vice-versa.

I.e. Certainly you must agree that:

1. voters must decide ONE way to cast their ONE ballot, and

2. it is not humanly possible to devine what ratings voters would give
to each candidate from looking at their approval voting ballots
because IF you are talking about APPROVAL voting, then there ARE NO
RATINGS, and you might agree that no one has superhuman powers to know
by looking at approval ballots, the ratings voters would give.

Chris, If you want to provide an example that makes a lick of sense
and does not assume that you can magically read all voters' minds, and
is logical and valid for EITHER approval or range voting which
exhibits the spoiler effect, then you must find an example that is
RANGE voting alone or an example which is APPROVAL voting that
exhibits the spoiler effect; or alternatively use only 0's and 1's to
signify your approval voting ratings.

Approval voting is analogous to giving a rating of 1 or 0, not the
example

Re: [Election-Methods] RELEASE: Instant Runoff Voting (Chris Benham)

[Chris Benham]

- Original Message 
From: Abd ul-Rahman Lomax [EMAIL PROTECTED]
To: Chris Benham [EMAIL PROTECTED]; EM election-methods@lists.electorama.com
Sent: Tuesday, 24 June, 2008 10:01:46 AM
Subject: Re: [Election-Methods] RELEASE: Instant Runoff Voting (Chris Benham)

At 12:55 AM 6/23/2008, Chris Benham wrote:
Kathy,

Imagine  that  Approval is used to elect the  US President and
as in the current campaign the Republicans  are fielding one
candidate, McCain.  Does that mean that the big fight for the
Democrat nomination between  Clinton and Obama we've just
seen would in the Approval scenario be completely unnecessary?

No. That fight is over the Democratic Party nomination and 
endorsement. It means that the whole apparatus of the Democratic 
Party is devoted to one candidate, which is, of course, strongly in 
the interest of the Democratic Party.
You know that that is somewhat beside the point. But I get the impression
that most of the money goes directly to the campaigns of the individual
candidates and that the media attention is mainly focused on the individual
candidates, rather than say  the policies of the Democratic Party irrespective
of who is their endorsed candidate.

Why not simply endorse both candidates?  After all, one cannot
possibly spoil the election for the other because Approval has
no spoiler problem. Voters simply approve candidates or not
completely regardless of what other candidates are on the ballot,
right?

Sure. If we imagine that somehow the parties have decided not to 
nominate candidates, snowballs in hell nevermind, running both Obama 
and Clinton against a single McCain would probaby result in very 
common double-voting. Now, if Obama and Clinton heavily campaign 
against each other, slinging mud, etc, trying to convince the voters 
that the other one is practically the devil, nobody would benefit 
from this except McCain. Which is quite why we don't do things this 
way. Parties in Australia don't run multiple candidates for the same 
single-winner office, do they?
No, but very closely allied candidates sometimes run against each other,
such as a candidate each from both Coalition partners (the Liberals and
the Nationals).  

The problem, were it Approval, wouldn't be so much the voting method. 
(Which, by the way, loses most of the problems it has if a majority 
is required or there is a runoff). It would be the rest of the 
system, the process by which voters become informed, or deluded, 
depending on your point of view.

I  think that in practical effect Approval  does have a spoiler or
split-vote problem  that would be sufficient for the Democrats to
still want to endorse one candidate only.

There are *lots* of reasons why the Democrats would want to do that. 
Or any party. This is a red herring argument. The split vote 
problem in Approval is a very different animal than the split vote 
problem in Plurality, or, for that matter, in IRV.
I don't see how the split-vote problem in Approval is a very different
animal than the split vote problem in Plurality.  To me it is just much
less severe. The split-vote problem in IRV  is much less and normally
unnoticable.
I think in the US scenario with voluntary voting, if  both Clinton and
Obama ran McCain would have less chance of winning with IRV
than with Approval or Range or Bucklin or any other reasonable
method that springs to mind. This is because both Clinton and
Obama have their enthusiastic supporters some of whom wouldn't
bother voting if their favourite wasn't running, but if their favourite
was running they would show up and (at the urging of their favourite)
rank both Clinton and Obama  above McCain.

IRV, meeting both Majority for Solid Coalitions and  Later-no-Harm
has no  defection  incentive like other methods.
http://lists.electorama.com/pipermail/election-methods-electorama.com/2006-November/018844.html


What I actually wrote in my initial post on the 5  fairness
principles in your paper (regarding IIA):

In practical effect  *no* method meets this.Approval and Range can 
be said to meet
Independence of Irrelevant Alternatives (IIA) only if the votes are 
interpreted as the voters giving
ratings on some fixed scale that is independent of the actual candidates.

No, that's not correct. Perhaps it would be useful if you actually 
state the version of IIA you are using. Usually, it refers to adding 
or subtracting a candidate without changing the preference order of 
the other candidates, but if you are going to use it with Range and 
Approval, you have to modify it; the basic modification is that the 
Range Votes or Approval Votes don't change, and all that happens is 
that a new candidate is added to the ballot or taken off the ballot.
If  the voters rate the candidates on some fixed scale that is independent
of the candidates, then by definition the Range or Approval votes would
be unchanged by adding (or removing) a candidate. What's not correct
about it?  

If voters are allowed to actually change

Re: [Election-Methods] RELEASE: Instant Runoff Voting - Not What It Seems

[Chris Benham]

Hello,
Continuing my commentry on Kathy Dopp's anti-IRV paper, under
Flaws of  Instant Runoff  Voting we find:
13. 
voters may not be allowed to participate in the final selection round of an IRV 
election
because all their choices were eliminated before the last counting round.

The only way voters  may not be allowed to participate in the final selection 
round
of an IRV election is if  they are restricted from ranking  as many candidates 
as they
wish, a restriction that I strongly oppose (and doesn't exist in Australia).

Presumably Kathy thinks it is a bad thing that some voters aren't allowed to 
participate
in the final IRV selection round, so we can logically infer that Kathy prefers 
IRV with
unrestricted ranking to IRV with restricted ranking, right?  Wrong. Further 
down the
paper she writes:Restricting the ranking depth of ranked choice ballots could 
improve IRV methods
by reducing noise and making it easier for voters.

Kathy, your hero Abd ul Lomax disagrees! He recently wrote:
If you are going to use a preferential ballot, with STV as the method, 
allowing full ranking is important.

 http://groups.yahoo.com/group/RangeVoting/message/8276

STV stands for  'Single Transferable Vote'.  IRV  is single-winner STV.

Chris BenhamNot all voters or ballots are treated equally: Unlike with actual 
runoff elections, some IRV


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Re: [Election-Methods] RELEASE: Instant Runoff Voting (Chris Benham) (tidied-up re-post)

[Chris Benham]

At 12:55 AM 6/23/2008, Chris Benham wrote:
Kathy,

Imagine  that  Approval is used to elect the  US President and
as in the current campaign the Republicans  are fielding one
candidate, McCain.  Does that mean that the big fight for the
Democrat nomination between  Clinton and Obama we've just
seen would in the Approval scenario be completely unnecessary?

Abd:
No. That fight is over the Democratic Party nomination and 
endorsement. It means that the whole apparatus of the Democratic 
Party is devoted to one candidate, which is, of course, strongly in 
the interest of the Democratic Party.

Chris:
 You know that that is somewhat beside the point. But I get the impression
that most of the money goes directly to the campaigns of the individual
candidates and that the media attention is mainly focused on the individual
candidates, rather than say  the policies of the Democratic Party irrespective
of who is their endorsed candidate.

Why not simply endorse both candidates?  After all, one cannot
possibly spoil the election for the other because Approval has
no spoiler problem. Voters simply approve candidates or not
completely regardless of what other candidates are on the ballot,
right?
Abd:
Sure. If we imagine that somehow the parties have decided not to 
nominate candidates, snowballs in hell nevermind, running both Obama 
and Clinton against a single McCain would probaby result in very 
common double-voting. Now, if Obama and Clinton heavily campaign 
against each other, slinging mud, etc, trying to convince the voters 
that the other one is practically the devil, nobody would benefit 
from this except McCain. Which is quite why we don't do things this 
way. Parties in Australia don't run multiple candidates for the same 
single-winner office, do they?
Chris:
 No, but very closely allied candidates sometimes run against each other,
such as a candidate each from both Coalition partners (the Liberals and
the Nationals).
Abd:  
The problem, were it Approval, wouldn't be so much the voting method. 
(Which, by the way, loses most of the problems it has if a majority 
is required or there is a runoff). It would be the rest of the 
system, the process by which voters become informed, or deluded, 
depending on your point of view.

I  think that in practical effect Approval  does have a spoiler or
split-vote problem  that would be sufficient for the Democrats to
still want to endorse one candidate only.

There are *lots* of reasons why the Democrats would want to do that. 
Or any party. This is a red herring argument. The split vote 
problem in Approval is a very different animal than the split vote 
problem in Plurality, or, for that matter, in IRV.
Chris:
 I don't see how the split-vote problem in Approval is a very different
animal than the split vote problem in Plurality.  To me it is just much
less severe. The split-vote problem in IRV  is much less and normally
unnoticable.
 
I think in the US scenario with voluntary voting, if  both Clinton and
Obama ran McCain would have less chance of winning with IRV
than with Approval or Range or Bucklin or any other reasonable
method that springs to mind. This is because both Clinton and
Obama have their enthusiastic supporters some of whom wouldn't
bother voting if their favourite wasn't running, but if their favourite
was running they would show up and (at the urging of their favourite)
rank both Clinton and Obama  above McCain.

IRV, meeting both Majority for Solid Coalitions and  Later-no-Harm
has no  defection  incentive like other methods.
 
http://lists.electorama.com/pipermail/election-methods-electorama.com/2006-November/018844.html
 


What I actually wrote in my initial post on the 5  fairness
principles in your paper (regarding IIA):

In practical effect  *no* method meets this.Approval and Range can 
be said to meet
Independence of Irrelevant Alternatives (IIA) only if the votes are 
interpreted as the voters giving
ratings on some fixed scale that is independent of the actual candidates.
Abd:
No, that's not correct. Perhaps it would be useful if you actually 
state the version of IIA you are using. Usually, it refers to adding 
or subtracting a candidate without changing the preference order of 
the other candidates, but if you are going to use it with Range and 
Approval, you have to modify it; the basic modification is that the 
Range Votes or Approval Votes don't change, and all that happens is 
that a new candidate is added to the ballot or taken off the ballot.

Chris:
 If  the voters rate the candidates on some fixed scale that is independent
of the candidates, then by definition the Range or Approval votes would
be unchanged by adding (or removing) a candidate. What's not correct
about it?  
Abd:
If voters are allowed to actually change their votes, *no method 
meets IIA.* Simple proof: there is a candidate whose name is a 
trigger for a long-hidden internal program that causes human beings 
to fall into a trance when they contemplate whether

Re: [Election-Methods] Dopp: 15. “Violates some election fairness principles .

[Chris Benham]

Kathy Dopp  quoted approvingly from  this Abd post
and told me off for not addressing it, so here goes.
Abd:
Later-No-Harm is FairVote's favorite election 
criterion. That's because the peculiar design of 
sequential elimination guarantees -- if a 
majority is not required -- that a lower 
preference cannot harm a higher preference, 
because the lower preferences are only considered 
if a higher one is eliminated. But later-no-harm 
is a quite controversial criterion, many think it positively undesirable.


CB:
Drop the pejorative peculiar, and replace many with 'some'  and
so far I don't have a problem .
Abd:
Woodall, who named Later-no-harm, wrote: ... 
Under STV the later preferences on a ballot are 
not even considered until the fates of all 
candidates of earlier preference have been 
decided. Thus a voter can be certain that adding 
extra preferences to his or her preference 
listing can neither help nor harm any candidate 
already listed. Supporters of STV usually regard 
this as a very important property, although it 
has to be said that not everyone agrees; the 
property has been described (by Michael Dummett, 
in a letter to Robert Newland) as quite 
unreasonable, and (by an anonymous referee) as unpalatable.

Indeed. Later-no-harm interferes with the process 
of equitable compromise that is essential to the 
social cooperation that voting is supposed to 
facilitate. 

CB:
I would say that voting depends on some already existing
social cooperation rather than being  necessarily designed
to facilitate it.  But in any case Later-no-Harm can help
facilitate such cooperation by at least removing the voters'
incentive to conceal their compromise choices.
Abd:
If I am negotiating with my neighbor, 
and his preferred option differs from mine, if I 
reveal that some compromise option is acceptable 
to me, before I'm certain that my favorite won't 
be chosen, it is utterly ruled out, then I may 
harm the chance of my favorite being chosen. If 
the method my neighbor and I used to help us make 
the decision *requires* later-no-harm, it will 
interfere with the negotiation process, make it 
more difficult to find mutually acceptable solutions.
CB:
One single person negotiating with another single person
isn't an apt comparison with public elections because with
just 2 voters the only options are compromise ('unanimity')
or an exact tie. 
Abd:
Later-no-harm is actually one of the few common 
criteria that IRV satisfies, along with the Majority Criterion.
CB:
I don't know why we should regard common criteria as
necessarily more important and interesting than uncommon
criteria. Elsewhere, in response to me listing criteria (that I
value) that are met by IRV(Alt.V, unlimited strict ranking)
but not Abd's preferred  Top-Two Runoff, Abd wrote:
Numbers of Criteria satisfied is a pretty bad measure of election performance.
http://groups.yahoo.com/group/RangeVoting/message/8249

Abd:
Sure, it's a possible argument that all voting methods 
violate some election fairness principles, but 
... Ms. Dopps statement still stands.
CB:
It is on a list of  Flaws of  Instant Runoff  Voting. It looks like 
propaganda aimed at people who might wrongly suppose or
assume that there is some voting method that *doesn't* violate
some election fairness priniples.
I hope this arrives in readable form. Probably more soon.
Chris Benham




Abd ul-Rahman Lomax  wrote (Fri Jun 13  2008): 

15. Dopp: “Violates some election fairness principles
.

This charge reveals either a general lack of 
understanding, or intentional 
miss-representation. Every single voting method 
ever devised must violate some fairness 
principles as some of these criteria are 
mutually exclusive. Dopp's example in appendix B 
of Arrow's fairness condition (the Pareto 
Improvement Criterion) completely misunderstands 
the criterion, and gives an example that has no 
relevance to it (and contrary to her 
implication, IRV complies with this criterion). 
IRV works essentially the same as a traditional 
runoff election to find a majority winner. When 
the field narrows to the two finalists in the 
final instant runoff count, the candidate with 
more support (ranked more favorably on more 
ballots) will always win. Some theoretical 
voting methods may satisfy some fairness' 
criteria, such as monotonicity, but then violate 
other more important criteria such as the 
majority criterion, or the later-no-harm criterion.

This is typical argument from FairVote. Read it 
carefully. Without going into the truth of the 
remainder of the paragraph, the remainder of the 
paragraph confirms what Ms. Dopp wrote. Sure, 
it's a possible argument that all voting methods 
violate some election fairness principles, but 
... Ms. Dopps statement still stands. There are a 
number of issues here, and it's something that 
has fooled even experts, so please bear with me.

Arrow's theorem has been widely interpreted as 
no election method is perfect, or all election 
methods must violate

Re: [Election-Methods] A Better Version of IRV?

[Chris Benham]

Forest Simmons wrote (Sun Jul 6 16:36:32 PDT 2008 ):

There is a lot of momentum behind IRV.  If we cannot stop it, are there some 
tweaks that would make it more liveable?
Someone has suggested that a candidate withdrawal option would go a long way 
towards ameliorating the damage.
Here's another suggestion, inspired by what we have learned from Australia's 
worst problems with their version of IRV:
Since IRV satisfies Later No Harm, why not complete the incompletely ranked 
ballots with the help of the rankings of the ballot's favorite candidate?
The unranked candidates would be ranked below the ranked candidates in the 
order of the ballot of the favorite.
If the candidates were allowed to specify their rankings after they got the 
partial results, this might be a valuable improvement.
Forest
Forest,
To me in principle voter's votes being commandeered by candidates isn't 
justified.
This particular horrible idea would create a strong incentive for the major 
power-brokers
to sponsor the nomination of a lot of fake candidates just to collect votes for 
one or other
of the major parties.

How do you think it might be a valuable improvement?  What scenario do you 
have in
mind? 
And what do you have in mind as  Australia's worst problems with their version 
of IRV?

Why do you want to stop IRV? Do you agree with Kathy Dopp  that  IRV is worse 
than 
FPP?
Chris Benham



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[Election-Methods] Dopp:17. Unstable and can be delicately sensitive to noise in the rankings.

[Chris Benham]

From Kathy Dopp's anti-IRV propaganda report:
 17. Unstable and can be delicately sensitive to noise in the rankings. If an 
election is not
resolved after 3 rounds of IRV then one is deep in the ranking for many people. 
This means
noise in the rankings. Do people really study candidates they don't care much 
about? Thus
the noise in the ranking for the most ill-informed voters is determining the 
outcome in deep
rank run-offs.
When a race is unresolved after 3 rounds of IRV, a better solution is to hold a 
real run off
with the remaining candidates. Having winnowed the field, voters can now 
properly study
their allowed few choices with the required care and presumably enough will to 
make the
outcome not contingent on noise. Moreover, can you fathom how awful it would be 
to fill
out a ballot ranking every candidate 10 deep? In Australia, voters are required 
by law to fill
rank ever candidate running (generally 20) from 1 to 20. Do you think there is 
anything
besides noise in the last ten? The saving grace on the Australian ballot is 
that generally there
are only 2 questions, one with 3 to 4 rankings and one with about 20. Not like 
our USA
ballots. Restricting the ranking depth of ranked choice ballots could improve 
IRV methods
by reducing noise and making it easier for voters. 

No-one I gather is suggesting that in the US voters should be compelled to 
fully rank, so all
this is silly crude stuff.
In Australia, voters are required by law to fill rank ever candidate running 
(generally 20) from 1 to 20.
The generally 20 figure is false. For Australian IRV elections there is 
rarely more than about
seven candidates.

The figure 20 is about right for elections to the Senate, which uses 
multi-member  STV
(corrupted into a quasi-list system).
Elsewhere in the paper we read that IRV is inadequate because it can't 
guarantee  that the
winner will be elected with the support of a majority of all the voters who 
submitted 
valid ballots.
Restricting the ranking depth of ranked choice ballots could improve IRV 
methods
by reducing noise and making it easier for voters.
But Kathy favours restricting ranking depth which of course has the effect of 
making
this avowed aim much less likely.
And of course restricting ranking doesn't make it easier for voters. If  
truncation is allowed,
how could it?  
In fact it just makes it harder for some voters. Say there are many candidates 
and I judge
that 2 of them are the front-runners, I have a preference between them but they 
are my
2 least favourite candidates. I am stuck with the same dilemma and strong 
incentive to use
the Compromise strategy that I have in FPP. To have some hope of having an 
impact on
the result I must insincerely rank my preferred front-runner above 
second-bottom.
Chris Benham


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Re: [Election-Methods] A Better Version of IRV?

[Chris Benham]

Forest,
The voter ranks all she wants to and the remaining candidates are ranked 
(later, i.e. below) by the voter's 
favorite or perhaps, as Steve Eppley has suggested, by the voter's specified 
public ranking. 

Since IRV satisfies LNH, what's the harm in this?.
The harm is that voter's votes are used to help candidates that the voters may 
not wish to help.
It offends the principle that the voter should be fully in control of his/her 
vote.
Giving some voters (candidates) the power to fully control their own vote and 
also to complete
the rankings of some of the truncators offends the principle that as far as 
possible all voters
should have equal power.
In Australia, where (in single winner elections) most of the voters copy 
candidate cards, this would save 
them a lot of bother.
In Australia the only significant bother stems from compulsory full strict 
ranking (for the vote to be
counted as valid).  How many or few voters choose to exercise their right to 
not follow their favourite's
ranking advice is no argument for removing that right.


This particular horrible idea would create a strong incentive 
for the major power-brokers to sponsor the nomination of a 
 lot of fake candidates just to collect votes for one or other
of the major parties.

Am I mising something here?
Yes, but I'm not sure exactly what.

I thought IRV was clone free.
It is, but that  isn't relevant.


How do you think it might be a valuable improvement?? What 
scenario do you have in mind?

(Besides the aboved mentioned advantage):

In conjunction with the candidate withdrawal option, it might enable the 
(other) losing candidates to save the 
Condorcet candidate, or otherwise compensate for IRV's non-monotonicity.

I've previously made my case against the candidate withdrawal option.

http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-March/021463.html

http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-March/021471.html

I don't see how IRV's failure to elect the Condorcet candidate is necessarily 
linked to its non-monotonicity.
There are monotonic (meets mono-raise) methods that fail Condorcet, and some 
Condorcet methods that
fail mono-raise.

I'm not impressed with embracing some evil definites in exchange for some vague 
mights.
And what do you have in mind as Australia's worst problems 
with their version of IRV?

It has degenerated into a defacto second rate version of Asset Voting.

To the extent that that is true it can (and should) be fixed by simply allowing 
truncation.

Why do you want to stop IRV? Do you agree with Kathy Dopp
that IRV is worse than FPP?

I would stop IRV if we could get a better method in its place.

If we cannot stop IRV, why not search for acceptable tweaks that would improve 
it?
The short answer is because IRV isn't really amenable to tweaks.  In terms 
of  positive
criterion compliances it isn't dominated by any other method, and has both good 
and quite
bad properties (averaging in my judgement to a good method).  Tweaks 
generally muck
up its good properties  without enough compensation in terms of fixing or 
patching up its
bad properties.
I think Smith (or Shwartz),IRV is quite a good  Condorcet method. It completely 
fixes the
failure of Condorcet while being more complicated  (to explain and at least 
sometimes to
count) than plain IRV, and a Mutual Dominant Third candidate can't be 
successfully buried.
But it fails Later-no-Harm and Later-no-Help, is vulnerable to Burying 
strategy, fails 
mono-add-top, and keeps  IRV's failure of  mono-raise and (related) 
vulnerability to
Pushover strategy.


It is better than FPP in some ways and worse in others, especially in 
complexity.
With separate paper ballots for each race, I don't accept that IRV is all that 
complex.
I think that you have somewhat dodged my question. 
 
Do you think that Asset Voting is worse than FPP?

No, on balance.

Just to clarify, I think that Condorcet Methods and Range, though better than 
IRV, share this complexity 
defect with IRV to some degree.  I have suggested the same tweak for them.  

In fact, that is the essence of DYN, wihich is simply carrying this tweak to 
its logical conclusion in the case 
of Range, which is the only one of the three (Range, Condorcet, and IRV) that 
satisfies the FBC.
I find your  DYN method  less offensive than your IRV tweak suggestion 
because it is an opt in system
and to the extent that voters don't opt in it is just plain Approval (a 
not-too-bad method).


Chris Benham






Forest Simmons  wrote (Fri Jul 11 15:11:38 PDT 2008 ):
 Forest Simmons wrote (Sun Jul 6 16:36:32 PDT 2008 ):  
 There is a lot of momentum behind IRV. If we cannot stop it, 
 are there some tweaks that would make it more liveable?
 Someone has suggested that a candidate withdrawal option would 
 go a long way towards ameliorating the damage.
 Here's another suggestion, inspired by what we have learned from 
 Australia's worst problems with their version

Re: [Election-Methods] A Better Version of IRV?

[Chris Benham]

At 02:01 AM 7/13/2008, Chris Benham wrote:
Forest,
The voter ranks all she wants to and the remaining candidates are 
ranked (later, i.e. below) by the voter's favorite or perhaps, as Steve 
Eppley has suggested, by the voter's specified public ranking.

Since IRV satisfies LNH, what's the harm in this?.

The harm is that voter's votes are used to help candidates that the 
voters may not wish to help.It offends the principle that the voter should 
be fully in control of his/her vote. Giving some voters (candidates) the 
power to fully control their own vote and also to complete the rankings of 
some of the truncators offends the principle that as far as possible all 
voters 
should have equal power.

Abd ul-Rahman Lomax wrote (Monday, 14 July, 2008) :

First of all, if we are talking about elections of representatives of 
some kind, the voter isn't going to be  in full control of his/her 
vote no matter what. At the point of the election, or later, when 
the representative casts votes, individual control is lost.
I'm afraid this is a typical bit of sophist blather from Abd. The type
of office that the election is for is completely irrelevant to the issue 
of whether or not voters in that election are fully in control of their
votes in that election. 

The equal power issue is spurious. The voting power is in the hands 
of those who cast ballots, originally, and they may choose to 
delegate that power or not. More about this below. The original 
candidate proxy or Asset Voting proposal was actually an STV 
proposal by Lewis Carroll, aka Charles Dodgson, in 1994.
In the proposal from Forest Simmons that I was addressing, the only
way a voter could choose not to delegate that power is to fully rank.
Any truncated ballots would be filled by the voter's voted favourite.

In Australia, where (in single winner elections) most of the voters 
copy candidate cards, this would save them a lot of bother.

In Australia the only significant bother stems from compulsory 
full strict ranking (for the vote to be counted as valid).  How many 
or few voters choose to exercise their right to not follow their favourite's
ranking advice is no argument for removing that right.

Compulsory full ranking, Dodgson noted, was a problem for voters who 
may not be sufficiently informed to understand how to rank *all* 
candidates. Obviously, full ranking only works when candidate count 
is limited, and even then donkey voting seems to be fairly common. It 
would be interesting to see statistics on straight sequence voting 
(which wouldn't be visible in Australian results because of Robson 
Rotation, one would have to look at actual ballots or true ballot images.)

Robson Rotation isn't used in any Australian IRV elections. As far as I
know it is only used in STV elections for multi-member districts in the 
state of  Tasmania and in the Australian Capital Territory.

  And what do you have in mind as Australia's worst problems
  with their version of IRV?

It has degenerated into a defacto second rate version of Asset Voting.
To the extent that that is true it can (and should) be fixed by 
simply allowing truncation.

That is done in Queensland and NSW, it's called Optional 
Preferential Voting, but, of course, in that there is no remedy for 
ballot exhaustion.
Ballot exhaustion isn't a problem, so doesn't need a remedy.



  Why do you want to stop IRV? Do you agree with Kathy Dopp
  that IRV is worse than FPP?

I would stop IRV if we could get a better method in its place.

If we cannot stop IRV, why not search for acceptable tweaks that 
would improve it?

The short answer is because IRV isn't really amenable to tweaks.  
In terms of  positive criterion compliances it isn't dominated by any other 
method, and has both good and quite bad properties (averaging in my judgement 
to a good method).  Tweaks generally muck up its good properties  
without enough compensation in terms of fixing or patching up its bad 
properties.

Problem is that the good property, Later No Harm, is actually a 
*terrible* property, see Woodall's original paper that coined the term.
Abd, thanks for the exact reference.
http://f1.grp.yahoofs.com/v1/UN16SP5h2KfHUAJcGXRtesX3hXxYWb9jBDf0yhOsY3xRy2NwboQ4Of2Ky67hAOHsd0xJ9c6iTYK1qZzZzVyKmJLN1lN_SFM/wood1994.pdf
In that paper there is nothing but a reference to the fact that not everyone 
agrees 
that it is desirable.  
Also, note that I wrote properties plural. 


There are other possible tweaks: for example, allow multiple votes in 
each rank.
Abd, as I've pointed out to you before this just makes IRV much more
vulnerable to Pushover strategy.
 
I think Smith (or Shwartz),IRV is quite a good  Condorcet method. It 
completely fixes the failure of Condorcet while being more complicated  
(to explain and at least sometimes to count) than plain IRV, and a Mutual 
Dominant 
Third candidate can't be successfully buried.
But it fails Later-no-Harm and Later-no-Help, is vulnerable to Burying 
strategy, fails
mono-add-top

Re: [Election-Methods] A Better Version of IRV?

[Chris Benham]

 I think Smith (or Shwartz),IRV is quite a good  Condorcet method. It 
 completely fixes the failure of Condorcet while being more complicated
 (to explain and at least sometimes to count) than plain IRV, and a Mutual
 Dominant Third candidate can't be successfully buried.
 But it fails Later-no-Harm and Later-no-Help, is vulnerable to Burying 
 strategy, fails mono-add-top, and keeps  IRV's failure of  mono-raise 
 and (related) vulnerability to Pushover strategy.

Kristofer Munsterhjelm  wrote (Sunday, 13 July, 2008 ):

At the risk of taking this thread away from its original topic, I wonder 
what you think of Smith,X or Schwartz,X where X is one of the methods 
Woodall says he prefers to IRV - namely QTLD, DAC, or DSC.

At one stage Woodall was looking for the method/s that meet as many of
his monotonicty properties as possible while keeping  Majority (equivalent
to Majority for Solid Coalitions).  That is what led him to Quota-Limited 
Trickle
Down (QLTD) and  then Descending Acquiescing Coalitions (DAC).
But I wouldn't conclude from this that for public political elections he 
currently
prefers those methods (or DSC) to IRV.


(Since QLTD is not an elimination method, it would go like this: first 
generate a social ordering. Then check if the ones ranked first to last 
have a Condorcet winner among themselves. If not, check if the ones 
ranked first to (last less one), and so on. As soon as there is a CW 
within the subset examined, he wins. Schwartz,QLTD would be the same but 
has a Schwartz set of just one member instead of has a CW.)

DAC and DSC only satisfy one of LNHelp/LNHarm, but they're monotonic in 
return. According to Woodall, you can't have all of LNHelp, LNHarm, and 
monotonicity, so in that respect, it's as good as you're going to get. I 
don't know if those set methods are vulnerable to burying, though, or if 
they preserve Mutual Dominant Third.

They  don't meet Mutual Dominant Third.
49: A
48: B
03: CB
The MDT winner is B, but DSC elects A.
03: D
14: A
34: AB
36: CB
13: C

The MDT winner is C, but DAC elects B.
This latter example (from Michael Harman, aka Auros) I think put 
Woodall off  DAC.  B is an absurd winner. Without the 3 ballots 
that ignore all the competitive candidates the majority favourite is C.

But of course Smith implies MDT. 
DSC and DAC aren't just monotonic (meet mono-raise), they meet
Participation (which of course is lost when combined with Smith/Schwartz
because Participation and Condorcet are incompatible).
I think all methods that meet Condorcet are vulnerable to Burial. By themselves
DSC is certainly vulnerable to burial (and has a 0-info. random-fill incentive) 
and
DAC has strong truncation incentive.

Your question about QLTD has been asked before:
http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2005-March/015367.html
http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2005-March/015369.html

Possibly more later,
Chris Benham


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Re: [Election-Methods] A Better Version of IRV? (Forest)

[Chris Benham]

 and the voter's receipt.

 In terms of  positive criterion compliances it isn't dominated by any other 
 method, 
 and has both good and quite bad properties (averaging in my judgement to a 
 good method).  
 Tweaks generally muck up its good properties  without enough compensation 
 in terms of 
 fixing or patching up its bad properties.

 I think Smith (or Shwartz),IRV is quite a good  Condorcet method. It 
 completely fixes the
 failure of Condorcet while being more complicated  (to explain  and at least 
 sometimes to
 count) than plain IRV, and a Mutual Dominant Third candidate can't be 
 successfully buried.

 But it fails Later-no-Harm and Later-no-Help, is vulnerable to  Burying 
 strategy, fails 
 mono-add-top, and keeps  IRV's failure of  mono-raise and (related) 
 vulnerability to
 Pushover strategy.
 
 
 It is better than FPP in some ways and worse in others, 
 especially in complexity.
 With separate paper ballots for each race, I don't accept that 
 IRV is all that complex.
 I think that you have somewhat dodged my question.

It doesn't seem too complex to you, but how about to the voters in public 
elections? Most of the ordinary 
voters that I have talked to agree with Lewis Carroll.  They would rather not 
have to fill out rankings.

Truncation should be allowed, so no-one has to fill out rankings if they 
don't want to.
Chris Benham


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Re: [Election-Methods] RELEASE: Instant Runoff Voting

[Chris Benham]

Aaron,
In an important respect, Condorcet is more natural than IRV: if a majority 
prefers Brad over Carter, this preference exists whether the voting system does 
anything with it, or even elicits enough information to determine that it 
exists. 
Yes, except that Condorcet is a criterion and  IRV is a method, and  more 
natural doesn't have a precise meaning.

Condorcet simply discovers and applies this preference. IRV, on the other 
hand, elicits enough information to discover it exists, but may decide to 
ignore it based purely on procedural grounds. There are no good reasons for 
this, ever.
IRV meets Later-no-Harm and  Later-no-Help and  is immune to Burial strategy, 
and these properties are incompatible with the Condorcet criterion.
Some people think these reasons are good. 
Core support is a bogus reason: every time IRV chooses someone other than 
the plurality winner you're letting an overall majority trump a comparison of 
core supporters. But other times IRV will fail to do this, for reasons that 
simply don't exist apart from the system itself.
Core support  is  IMO just propaganda designed to reassure the public that 
IRV isn't  too radical a change from FPP.
BTW, which of the many methods that meet the Condorcet criterion is your 
favourite? 
Chris Benham


Aaron Armitage  wrote (Sun Jul 27,2008): 
Of course every reason you might offer for choosing one system over another is 
based on an idea of what a reasonable decision rule for making collective 
decisions in very large groups should look like. This is true for IRV advocate 
no less than advocates for other systems; where the system came from is beside 
the point, especially since most jurisdictions have never used the Exhaustive 
Ballot.

In an important respect, Condorcet is more natural than IRV: if a majority 
prefers Brad over Carter, this preference exists whether the voting system does 
anything with it, or even elicits enough information to determine that it 
exists. Condorcet simply discovers and applies this preference. IRV, on the 
other hand, elicits enough information to discover it exists, but may decide to 
ignore it based purely on procedural grounds. There are no good reasons for 
this, ever. Core support is a bogus reason: every time IRV chooses someone 
other than the plurality winner you're letting an overall majority trump a 
comparison of core supporters. But other times IRV will fail to do this, for 
reasons that simply don't exist apart from the system itself.


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Re: [Election-Methods] strategic voting and strategic nomination

[Chris Benham]

James,
Regarding the Alternative Vote (aka IRV) you wrote:
It is used for elections to the lower houses of Australia and Ireland, for 
mayoral
elections in England, and for local elections in about twelve American cities.

In Ireland it is used to elect the President. The Irish lower house uses 
multi-winner
STV.  UK mayoral elections mostly use the  Supplementary Vote. From Wikipedia:

The Supplementary Vote system is used for all mayoral elections in England and 
Wales. 
Under this system voters express a first choice and (optionally) a second 
choice. If no 
candidate receives 50% of first choice votes, the top two candidates go to a 
second round. 
Voters whose first choice has been eliminated but whose second choice is one of 
the top two 
candidates have their second preference vote added to the first-round totals 
for the leading 
candidates.

Of course it is equivalent to IRV when there are three candidates, but is 
otherwise awful.
Regarding MinMax in your paper you wrote:

The winner is the candidate whose worst pairwise loss (if any) is least 
bad;...
You don't define here how you measure least bad. Later you give this:
MinimaxTo calculate the winner1. Form a pairwise matrix. Form the 
greatest number of votes against x in any pairwise contest, i.e. 
candidate with the smallest value in the 
This make no reference to pairwise losses, so isn't it  MinMax(Pairwise 
Opposition) that
*fails* the Condorcet criterion?
http://nodesiege.tripod.com/elections/#methmmpo
N by 1 vector MAXBEAT, where MAXBEATx is theMAXBEATx=max(PM:,x). TheMAXBEAT 
vector is the winner.
Chris Benham


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Re: [EM] Can someone point me at an example of the nonmonotonicity of IRV?

[Chris Benham]

Kathy Dopp wrote (Sat. Aug.10):
Well perhaps there are other voting methods where ranking my first
choice candidate below my last choice candidate helps my first choice
candidate to win more than vice-versa, and I would oppose any method
that did that.

Kathy,
What exactly do mean here by more than vice-versa?  Obviously in IRV
the voter probabilistically helps his/her sincere first choice candidate X to 
win
by ranking  X above his/her last choice candidate Y  (and for that matter all
other candidates) massively more than vice-versa.


Out of curiosity, what voting system would you recommend? I'm not saying
don't say anything if you don't have an alternative, I'm just curious.

'I am currently not recommending *any* until I have more time and
inclination to sit down to thoroughly study all the alternatives. I
know that IRV is a really bad method as applied to real life
elections, and I suspect that most other voting methods are superior
to IRV in crucial ways that would make them more practical and
desirable.

My investigation of voting methods has led me to the conclusions that
(a) the best  voting methods are much worse than people new to the
field tend to assume, and
(b) there are many more desirable/interesting/useful  voting methods
criteria possible (and proposed) than people tend to assume or are 
aware of.
These factors make it quite easy for someone who refuses to stand by any
one method to make propaganda against any given method simply by dwelling
on and emphasizing its negatives and ignoring (as much as plausibly possible)
mentioning criteria that it meets.

This stance of yours leads one to suspect that your real voting methods agenda
is simply to defend the FPP status quo, and  that you are so virulently 
attacking
IRV because that is the alternative with the most traction as a practical reform
proposal.
Chris Benham


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Re: [EM] Can someone point me at an example of the nonmonotonicity of IRV?

[Chris Benham]

Kristofer Munsterhjelm  wrote (Sun. Aug.10):

There's also the it smells fishy that nonmonotonicity - of any kind or 
frequency - evokes. I think that's stronger for nonmonotonicity than for 
things like strategy vulnerability because it's an error that appears in 
the method itself, rather than in the move-countermove game brought on 
by strategy, and thus one thinks if it errs in that way, what more 
fundamental errors may be in there that I don't know of?. But that 
enters the realm of feelings and opinion.
Kristopher,
The intution or  feeling you refer to is based on the idea that the best 
method/s
must be mathematically elegant and that methods tend to be consistently good
or consistently bad.

But in the comparison among reasonable and  good methods, this idea is wrong.
Rather it is the case that many arguably desirable properties (criteria 
compliances)
are mutually incompatible. So on discovering that  method X has some 
mathematically
inelegant or paradoxical flaw one shouldn't immediately conclude that  X  must 
be
one of  the worst methods.  That flaw may enable X to have some other 
desirable
features.
To look at it the other way, Participation is obviously interesting and viewed 
in isolation
a desirable property. But I know that it is quite expensive, so on 
discovering that method
Y meets Participation I know that it must fail other criteria (that I value) 
so  I don't expect
Y  to be one of my favourite methods.  

I think that all methods that work by calculating the ranking according 
to a positional function, then eliminating one or more candidates, then 
repeating until a winner is found will suffer from nonmonotonicity. I 
don't know if there's a proof for this somewhere, though.

A positional function is one that gives a points for first place, b 
points for second, c for third and so on, and whoever has the highest 
score wins, or in the case of elimination, whoever has the lowest score 
is eliminated.

Less abstractly, these methods are nonmonotonic if I'm right: Coombs 
(whoever gets most last-place votes is eliminated until someone has a 
majority), IRV and Carey's Q method (eliminate loser or those with below 
average plurality scores, respectively), and Baldwin and Nanson (the 
same, but with Borda).
That's right, but I think that Carey's method  (that I thought was called 
Improved FPP)
is monotonic (meets mono-raise) when there are 3 candidates (and that is the 
point of it.)

It may be that this can be formally proven or extended to other 
elimination methods. I seem to remember a post on this list saying that 
Schulze-elimination is just Schulze, but I can't find it. If I remember 
correctly, then that means that not all elimination methods are 
nonmonotonic.
Of course Schulze isn't a positional function.  Obviously if there are just 3 
candidates in
the Schwartz set then Schulze-elimination must equal Schulze, but maybe there 
is some
relatively complicted example where there are more than 3 candidates in the top 
cycle
where the two methods give a different result.
Chris Benham


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[EM] Range-Approval hybrid

[Chris Benham]

I  have an idea for a  FBC complying method  that  I think is clearly
better  than the version of   Range Voting (aka  Average Rating or
Cardinal Ratings)  defined and promoted by  CRV.

  http://rangevoting.org/

I suggest that voters use multi-slot ratings ballots that have the bottom
slots (at least 2 and not more than half) clearly labelled as expressing
disapproval and all others as expressing Approval.  The default
rating is the bottom-most.

Compute each candidate X's  Approval score and also Approval
Opposition score  (the approval score of the most approved candidate
on ballots that don't approve X). 

All candidates whose approval score is exceeded by their approval
opposition (AO) score are disqualified.  Elect the undisqualified
candidate that is highest ordered by Average Rating.

I suggest many fewer slots than 99  and no  no opinion option, so I
think the resulting method is not more complex for voters.

This method would work much better than normal RV in avoiding a
split-vote problem in a  '2 sub-factions confront a big faction' scenario
(such as  Obama and  Clinton versus McCain).  In this method  if  Obama
and Clinton supporters all approve both candidates and not McCain,
then if there are more of them voting than McCain supporters McCain
must be disqualified, so  Obama and Clinton can compete with each
other more meaningfully and with much less risk of  a McCain win.

Minor party supporters can make approval distinction between the 
front-runners and then rate their sincere favourites exclusive-top with
very little added risk  (compared with rating their preferred front-runner
equal-top) of  allowing their greater evil candidate to win.

It meets a sort of   Approval Strong Minimal Defense that says that
if more voters approve  X and not Y than approve Y, Y can't win.

And a sort of  Approval Majority for Solid Coalitions that says that
if  more than half  the voters rank/rate a subset S of candidates above
all others, and approve all the members of  S and none of the non-members,
then the winner must come from S. 

(This of course is only worth mentioning because the voters supporting
the S candidates can still make meaningful preference distinctions among
them, unlike in plain Approval.) 

Like normal Range it clearly meets Favourite Betrayal, because if  X wins
with some voters insincerely down-rating Y, then if  Y is raised to the top
slot alongside X; X will still be qualified (because X's approval score will
not be reduced and X's AO score can only be reduced), no non-XY candidate
can have a reduced PO score so no previously disqualified non-XY candidate
will become undisqualified; and of course only Y's  Average Ratings score
will be changed so if there is a  new winner it can only be Y.

Like normal Range and unlike  methods such  as  Bucklin, it meets Independence
from Irrelevant Ballots (IIB). This wouldn't be the case if  the rule regarding 
the
approvals specified for example that candidates need to be disapproved by a
majority to be disqualified.

I can't see that this method fails any desirable criterion that normal Range 
meets.

Comments?

Chris  Benham


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[EM] Fw: Range-Approval hybrid

[Chris Benham]

Chris Benham wrote:
 I  have an idea for a  FBC complying method  that  I think is clearly
 better  than the version of  Range Voting (aka  Average Rating or
 Cardinal Ratings)  defined and promoted by  CRV.
 
  http://rangevoting.org/
  
 I suggest that voters use multi-slot ratings ballots that have the bottom
 slots (at least 2 and not more than half) clearly labelled as expressing
 disapproval and all others as expressing Approval.  The default
 rating is the bottom-most.
  
 Compute each candidate X's  Approval score and also Approval
 Opposition score  (the approval score of the most approved candidate
 on ballots that don't approve X).
  
 All candidates whose approval score is exceeded by their approval
 opposition (AO) score are disqualified.  Elect the undisqualified
 candidate that is highest ordered by Average Rating.
  
 I suggest many fewer slots than 99  and no  no opinion option, so I
 think the resulting method is not more complex for voters.


Kristofer Munsterhjelm  wrote (Monday, 29 September, 2008):
One way of making it less complex would be to have a cardinal ratings 
(Range) ballot with both positive and negative integers. The voter rates 
every candidate, and those candidates that get below zero points are 
considered disapproved, while those that get above zero are considered 
approved. This idea doesn't specify where those rated at zero (or those 
not rated at all) would appear.

Yes. I suggest that those not rated should be interpreted as disapproved
and bottom-most rated.  Those candidates rated zero should be considered
to be half-approved. Candidate X's approval opposition to Y should be X's 
approval
score (including of course the half-approvals) plus half  X's approval score 
(likewise)
on ballots that rate Y zero.  Y's  Approval Oppostion score refers to Y's 
maximum approval opposition score from any X.


Normalization could be used if required, with either the voter 
specifying absolutely worst and absolutely best (setting the range), 
or by the lowest and highest rated candidate having those positions. So 
if a voter wants to say that he likes all the candidates, but some are 
better than others, he could vote all positive integers, whereas a 
McCain/Obama/Clinton voter could vote McCain less than zero and the 
other two greater than zero. With normalization, the contribution of

A: 1 pts.
B: -1 pts.

to the raw scores would be the same as

A: 3 pts.
B: 1 pt.

but would have a different effect regarding the approval component (only 
A approved in the first case, both approved in the second).


I don't think I'm that keen on normalization, but I don't really object to
'automating' the approval cutoff, so that ballots are interpreted as approving
the candidates they rate above the mean of  the ratings they've given (and
half-approving those exactly at that mean).  I can imagine that others would
object on various grounds, and the US voting reform enthusiasts who like
FBC-complying methods like Range and Approval generally seem to prefer 
their voting methods to have  'manual transmission'.

Chris Benham



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Re: [EM] Range-Approval hybrid

[Chris Benham]

Kristofer Munsterhjelm:

 Normalization could be used if required, with either the voter 
 specifying absolutely worst and absolutely best (setting the
 range), or by the lowest and highest rated candidate having those
 positions. So if a voter wants to say that he likes all the
 candidates, but some are better than others, he could vote all
 positive integers, whereas a McCain/Obama/Clinton voter could vote
 McCain less than zero and the other two greater than zero. With
 normalization, the contribution of
 
 A: 1 pts. B: -1 pts.
 
 to the raw scores would be the same as
 
 A: 3 pts. B: 1 pt.
 
 but would have a different effect regarding the approval component
 (only A approved in the first case, both approved in the second).
 

 Chris Benham:

 I don't think I'm that keen on normalization, but I don't really
 object to 'automating' the approval cutoff, so that ballots are
 interpreted as approving the candidates they rate above the mean of
 the ratings they've given (and half-approving those exactly at that
 mean).  I can imagine that others would object on various grounds,
 and the US voting reform enthusiasts who like FBC-complying methods
 like Range and Approval generally seem to prefer their voting methods
 to have  'manual transmission'.

Kristofer Munsterhjelm  wrote (Wednesday, 1 October, 2008):

The advantage of having zero set the boundary between approved and 
disapproved, instead of the mean doing so, is that you could express a 
general favor (or dislike) of politicians. For instance, if you think 
only one person's mostly decent and the rest are all corrupt (but some 
are more corrupt than others), you could vote the favored candidate 
above zero and the others below zero, whereas above mean would include 
some of the corrupt candidates as well.

CB: I don't see why it would. If  the voter max rates her favourite and gives
all the other candidates a much lower, near or absolute bottom rating then
the 'automated' version will only approve her favourite.

KM:
I can understand that some would prefer the ballot to have, to use your 
own words, a manual transmission, but I think the concept of an explicit 
approval cutoff would be confusing to most. With the boundary at 0, you 
can just say, implicitly, give those who you like points, and take 
points away from those you don't like.

When Approval voting has better strategies than plain commonsense 
approval, that's going to be a suboptimal strategy, but hopefully the 
voters are going to be mostly honest so that that's not much of a problem.

CB:
With Approval cutoffs my basic assumption is that voters will be strategic
and I'm happy for them to be so.  I generally like to try to minimise the 
advantage of good strategists over poor ones and non-strategists, so I'm
not interested in expanding voters' options to use poor strategy.

Chris  Benham



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Re: [EM] nge-Approval hybrid

[Chris Benham]

Chris Benham wrote:
I  have an idea for a  FBC complying method  that  I think is clearly
better  than the version of  Range Voting (aka  Average Rating or
Cardinal Ratings)  defined and promoted by  CRV.

  http://rangevoting.org/
  
I suggest that voters use multi-slot ratings ballots that have the bottom
slots (at least 2 and not more than half) clearly labelled as expressing
disapproval and all others as expressing Approval.  The default
rating is the bottom-most.
  
Compute each candidate X's  Approval score and also Approval
Opposition score  (the approval score of the most approved candidate
on ballots that don't approve X).
  
All candidates whose approval score is exceeded by their approval
opposition (AO) score are disqualified.  Elect the undisqualified
candidate that is highest ordered by Average Rating.
  
I suggest many fewer slots than 99  and no  no opinion option, so I
think the resulting method is not more complex for voters.


Kristofer Munsterhjelm  wrote (Monday, 29 September, 2008):
One way of making it less complex would be to have a cardinal ratings 
(Range) ballot with both positive and negative integers. The voter rates 
every candidate, and those candidates that get below zero points are 
considered disapproved, while those that get above zero are considered 
approved. This idea doesn't specify where those rated at zero (or those 
not rated at all) would appear.


CB:  Thinking about this method idea more, as a practical proposition either
a very simple way of handling the zero on a scale that includes negative and
positive numbers or not having a zero would be better.

One tidy relatively simple version would use a  A B C | D E F graded ballot
with  ABC shown on the ballot as taken to signify  approved or acceptable
and DEF  not.   

This could perhaps be promoted as  Graded Approval.  My technical name
for the method is I suppose  Approval Strong Minimal Defense, CR.

Chris Benham


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Re: [EM] nge-Approval hybrid

[Chris Benham]

Chris Benham wrote:
I  have an idea for a  FBC complying method  that  I think is clearly
better  than the version of  Range Voting (aka  Average Rating or
Cardinal Ratings)  defined and promoted by  CRV.

  http://rangevoting.org/
  
I suggest that voters use multi-slot ratings ballots that have the bottom
slots (at least 2 and not more than half) clearly labelled as expressing
disapproval and all others as expressing Approval.  The default
rating is the bottom-most.
  
Compute each candidate X's  Approval score and also Approval
Opposition score  (the approval score of the most approved candidate
on ballots that don't approve X).
  
All candidates whose approval score is exceeded by their approval
opposition (AO) score are disqualified.  Elect the undisqualified
candidate that is highest ordered by Average Rating.
  
I suggest many fewer slots than 99  and no  no opinion option, so I
think the resulting method is not more complex for voters.


Kristofer Munsterhjelm  wrote (Monday, 29 September, 2008):
One way of making it less complex would be to have a cardinal ratings 
(Range) ballot with both positive and negative integers. The voter rates 
every candidate, and those candidates that get below zero points are 
considered disapproved, while those that get above zero are considered 
approved. This idea doesn't specify where those rated at zero (or those 
not rated at all) would appear.


CB:  Thinking about this method idea more, as a practical proposition either
a very simple way of handling the zero on a scale that includes negative and
positive numbers or not having a zero would be better.

One tidy relatively simple version would use a  A B C | D E F graded ballot
with  ABC shown on the ballot as taken to signify  approved or acceptable
and DEF  not.   

This could perhaps be promoted as  Graded Approval.  My technical name
for the method is I suppose  Approval Strong Minimal Defense, CR.

Chris Benham


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[EM] IRV vs Condorcet vs Range/Score

[Chris Benham]

Dave Ketchum wrote:
I started this thread to compare IRV vs Condorcet, believing that IRV is 
provably less capable and deserves discarding.

Dave,
Comparing a decisive method  with a criterion is a bit like comparing a
person with  virtue.  As soon as you tell us which  *decisive method*
you support  I will be happy to discuss its comparison with IRV.

Or failing that, perhaps you could give us some clue as to what method
you support by telling us some other criteria besides the Condorcet Criterion
that you think a method should meet.

Chris Benham



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[EM] IRV vs Condorcet vs Range/Score

[Chris Benham]

Aaron,
I agree that not electing a voted CW is undesirable, and any method
that fails the Condorcet criterion needs to be justified by complying
with at least one desirable criterion that isn't compatible with Condorcet.

Low social utility (SU) Condorcet winners with little solid support and
depend for their status as the CW on weakly-held lower preferences can
begin to look quite chimera-like and not necessarily the only legitimate
winner.

One ok Condorcet method is Smith,IRV: voters strictly rank from the 
top however many candidates they wish, before each normal IRV 
elimination check for a candidate X that pairwise beats all the other 
remaining candidates, elect the first such X to appear.

Is this what you mean by Smith/IRV? Or did you mean Smith//IRV?

I'm not sure if you suggested otherwise, but all methods that meet the
Condorcet criterion are vulnerable to Burial strategy.

Chris Benham

 

Aaron Armitage wrote (Sat.Oct.11):
Condorcet methods are the application of majority rule to elections which
have more than two candidates and which cannot sequester the electorate
for however many rounds it takes to produce a majority first-preference
winner. If we consider majoritarianism an irreducible part of democracy,
then any method which fails to elect the CW if one exists is unacceptable.

Which particular method is chosen depends on what you want it to do. For
example, if we at to make it difficult to change the outcome with
strategic voting Smith/IRV would be best, because most strategic voting
will be burying a potential CW to create an artificial cycle in the hopes
that a more-preferred candidate will be chosen by the completion method. A
completion method which is also vulnerable to burial makes this worse, but
Smith/IRV isn't because it breaks the cycle in a way the ignores all
non-first rankings.


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[EM] Range-Approval hybrid

[Chris Benham]

Yet another version of this  Approval Strong Sincere Defense, Range
method occurs to me:  uses ratings ballots with more available slots than
there are candidates and on each ballot interpret the highest empty slot
as the approval threshold.

This is simpler than my previous automatic version which on each ballot
interpreted rating above mean as approval, but can still use the same type
of ballot as highish-resolution  Range/Score/CR.

Chris Benham


 

Chris Benham wrote:
I  have an idea for a  FBC complying method  that  I think is clearly
better  than the version of  Range Voting (aka  Average Rating or
Cardinal Ratings)  defined and promoted by  CRV.

  http://rangevoting.org/
  
I suggest that voters use multi-slot ratings ballots that have the bottom
slots (at least 2 and not more than half) clearly labelled as expressing
disapproval and all others as expressing Approval.  The default
rating is the bottom-most.
  
Compute each candidate X's  Approval score and also Approval
Opposition score  (the approval score of the most approved candidate
on ballots that don't approve X).
  
All candidates whose approval score is exceeded by their approval
opposition (AO) score are disqualified.  Elect the undisqualified
candidate that is highest ordered by Average Rating.
  
I suggest many fewer slots than 99  and no  no opinion option, so I
think the resulting method is not more complex for voters.


Kristofer Munsterhjelm  wrote (Monday, 29 September, 2008):
One way of making it less complex would be to have a cardinal ratings 
(Range) ballot with both positive and negative integers. The voter rates 
every candidate, and those candidates that get below zero points are 
considered disapproved, while those that get above zero are considered 
approved. This idea doesn't specify where those rated at zero (or those 
not rated at all) would appear.


CB:  Thinking about this method idea more, as a practical proposition either
a very simple way of handling the zero on a scale that includes negative and
positive numbers or not having a zero would be better.

One tidy relatively simple version would use a  A B C | D E F graded ballot
with  ABC shown on the ballot as taken to signify  approved or acceptable
and DEF  not.   

This could perhaps be promoted as  Graded Approval.  My technical name
for the method is I suppose  Approval Strong Minimal Defense, CR.

Chris Benham


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[EM] Worst Voting Method

[Chris Benham]

I don't see antiplurality as much worse than FPP.

Antiplurality  (vote against one, candidate with fewest votes wins) meets
Majority Loser  and  Strong Favourite  Betrayal.

Very bad is the Supplementary Vote used to elect some mayors in the 
UK.   It is like the Contingent Vote  (one trip to the polls TTR) except
voters are only allowed to rank 2 candidates.

Borda Voting is also very bad.  It fails  Majority Favourite and  Rich Party
(meaning that it fails Clone-Loser in a way that advantages factions who field
more candidates).

Chris Benham

 
 
 
Greg Nisbet  wrote:
What is the worst voting method of all time?

I suggest methods already made up

I suggest antiplurality, if that doesn't count, then... hmmm... North
Carolina's weird version of IRV.
http://www.fairvote.org/irv/?page=21articlemode=showspecificshowarticle=2229

40% to win? 40%?! WHY?



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Re: [EM] Worst Voting Method

[Chris Benham]

Very bad is the Supplementary Vote used to elect some
mayors in the  UK.   It is like the Contingent Vote  (one trip to 
the polls TTR) except voters are only allowed to rank 2 candidates.


Kevin Venzke wrote:

I don't see how this is very bad. I could see how you might think it
is easily improved. But is this method better or worse than Approval? Is 
it better or worse than FPP?

Kevin,
The question of the precise ranking of  the worst single-winner methods
doesn't interest me very much. I just mentioned it as a method in use with
absurd arbitrary features/restrictions that is dominated (in terms of useful 
criterion 
compliances) by IRV.

To reluctantly answer your question I suppose it isn't worse than FPP  and
is probably worse than Approval.

I'd be much more interested in your reaction to my recent Range-Approval
hybrid suggested methods, which after all use the concept of  Approval
Opposition which you invented.

Chris Benham

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[EM] 3-slot SMD,ER-FPP(w)

[Chris Benham]

I have an idea for a new 3-slot voting method:

*Voters fill out 3-slot ratings ballots, default rating is bottom-most
(indicating least preferred and not approved).

Interpreting top and middle rating as approval, disqualify all candidates
with an approval score lower than their approval-opposition (AO) score.
(X's  AO score is the approval score of the most approved candidate on
ballots that don't approve X).

Elect the undisqualified candidate with the highest top-ratings score.*

This clearly meets Favourite Betrayal, Participation, mono-raise, mono-append,
3-slot Majority for Solid Coalitions, Strong Minimal Denfense (and so Minimal
Defense and  Woodall's Plurality criterion), Independence of  Irrelevant 
Ballots.

This  3-slot Strong Minimal Defense, Equal-Ranking First-Preference Plurality 
(Whole) method is my new clear favourite 3-slot single-winner method.

One small technical disadvantage it has compared to Majority Choice Approval 
(MCA)
and  ER-Bucklin(Whole) and maybe Kevin Venzke's ICA method is that it fails
what I've been calling Possible Approval Winner (PAW).

35: A
10: A=B
30: BC
25: C

Approval scores:  A45,   B40,  C55
Approval Opp.:    A55,  B35,   C45
Top-ratings score: A45,  B40,   C25.  

C's approval opposition to A is 55, higher than A's approval score of 45, so A 
is
disqualified.  The undisqualified candidate with the highest top-ratings score 
is B,
so B wins.  But if we pretend that on each ballot there is an invisible approval
threshold that makes some distinction among the candidates but not among those
with the same rank, then B cannot have an approval score as high a A's.

This example is from Kevin Venzke, which he gave to show that Schulze (also) 
elects
B and so fails this criterion.  It doesn't bother me very much. MCA and  
Bucklin elect
C.

It is more Condorcetish and has a less severe later-harm problem than MCA, 
Bucklin,
or  Cardinal Ratings (aka Range, Average Rating, etc.)

40: AB
35: B
25: C

Approval scores:    A40,   B75,   C25 
Approval Opp.:  A35,   B25,   C75
Top-ratings scores: A40,   B35,   C25 

They elect B, but SMD,FPP(w) elects the Condorcet winner A.

It seems a bit less vulnerable to Burial strategy than Schulze.

46: AB
44: BC  (sincere is BA)
05: CA
05: CB

Approval scores:    A51,   B95,   C54 
Approval Opp.:  A49,   B05,   C46
Top-ratings scores: A46,   B44,   C10.  

In this admittedly not very realistic scenario, no candidate is disqualified 
and so A
wins. Schulze elects the buriers' favourite B.


Chris  Benham

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[EM] 3-slot SMD,ER-FPP(w)

[Chris Benham]

--- En date de : Dim 19.10.08, Chris Benham cbenhamau at yahoo.com.au a 
écrit :
I have an idea for a new 3-slot voting method:

*Voters fill out 3-slot ratings ballots, default rating is
bottom-most (indicating least preferred and not approved).

Interpreting top and middle rating as approval, disqualify
all candidates with an approval score lower than their approval-opposition
(AO) score.
(X's  AO score is the approval score of the most approved candidate on
ballots that don't approve X).

Elect the undisqualified candidate with the highest
top-ratings score.*
 Kevin Venzke wrote (Mon.Oct.20):


Interesting method, but I'm concerned that rating a candidate in the 
middle can disqualify other candidates, but can't help this candidate 
win, except by preventing him from being disqualified himself. It seems
like a burial risk.

With two major factions supporting A and B, and a third candidate C,
if A faction buries B under C, I believe A will often win. Does B faction
have a defensive strategy that isn't the same as the offensive strategy?
I don't think they do.

Actually, this method isn't that far from MDD,FPP.

CB: Except that method fails Irrelevant Ballots and I think meets LNHarm.

This clearly meets Favourite Betrayal, Participation,
mono-raise, mono-append,
3-slot Majority for Solid Coalitions, Strong Minimal
Denfense (and so Minimal
Defense and  Woodall's Plurality criterion),
Independence of  Irrelevant Ballots.

I don't think it satisfies Participation, because your favorite candidate
could be winning, and when your vote is added, you add sufficient
approval to your compromise choice that they are no longer disqualified,
and are able to win instead of your favorite.

CB: Oops!.. you are right. It fails Participation and even Mono-add-Top.

8: C
3: F
2: XF
2: YF
2: ZF

F wins after all other candidates are disqualified, but if  2 FC ballots are
added C wins in exactly the way you describe.

It looks like the Strong Minimal Defense mechanism is incompatible with
Participation, so I was also wrong in suggesting that my recent Range-Approval
hybrid method suggestion meets Participation.

I still like this 3-slot SMD,FPP(w) method however and am confident the other
criterion compliances I claimed for it hold up.


Chris Benham

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[EM] About Condorcet//Approval

[Chris Benham]

Kristofer Munsterhjelm  wrote (Sat.Oct.18):
Because Smith is more complex to explain, my current favorite election 
method is Condorcet//Approval. We don't need complex algorithms to find a 
winner.

You could also have the approval version of Smith,IRV. Call it 
Condorcet,Approval. I think it's Smith (so it would be Smith,Approval), 
but I'm not sure. The method is this: Drop candidates, starting with the 
Approval loser and moving upwards, until there's a CW. Then that one is 
the winner.

 
Kristofer,
The method you describe isn't Smith,Approval (which is the same thing as
Smith//Approval).  Smith,Approval elects the member of the Smith set
highest-ordered by Approval on the original ballots, Smith//Approval first
eliminates (drops from the ballots) all non-members of the Smith set and
applies Approval to the remaining candidates. 

Since approval is treated as 'absolute' it doesn't make a difference like it 
does 
between Smith,IRV and Smith//IRV.
 
The method you describe has IRV-like mono-raise failure and Pushover 
strategy vulnerability.
 
31: AB
32: BC
31: CA
06: C
 
All ranked candidates are approved, and all candidates are in the Smith set.
AB 62-32,   BC 63-31,  CA 69-31.   
Approval scores:  A62,  B63,  C69.

A is eliminated and B wins, but if  2 of  the 6 C votes change to A then C 
wins. 
 
31: AB
32: BC
31: CA
04: C
02: A
 
The Approval winner C is the clearly strongest candidate (the most first 
preferences 
and the most second preferences) in both cases.
 
These methods would obviously need approval cutoff ballots (unless you 
go with the MDDA assumption, that the approval cutoff is where the voter 
truncates, but I don't think that would be a good idea here).

Here I agree with Kevin Venzke. Allowing voters to rank among candidates they
don't approve just makes the method more vulnerable to Burial strategy and makes
the proposal much more complex.
 
 
Chris Benham

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[EM] About Condorcet//Approval

[Chris Benham]

Kevin,
I think the version of  DMC  that allows voters to rank among unapproved
candidates fails mono-raise, and both versions are vulnerable to Pushover
strategy. 

Would you say that that the plain all ranked are approved version
doesn't properly fail mono-raise but instead fails mono-raise-delete?

http://lists.electorama.com/pipermail/election-methods-electorama.com/2007-March/019824.html

I wrote in March 2007:
With the approval cutoffs, DMC  (and AWP) come close to failing mono-raise.

31: AB
04: AC
32: BC
33: CA

ABCA   Approvals: A35,  B32,   C33. 
A eliminates (doubly defeats) B, and C wins. (AWP measures 
defeat-strengths by the number of ballots on the winning side that approve the 
winner and not the loser, and so says C's defeat is the weakest and so also
elects C.)

Now change the 4 AC ballots to CA

31: AB
32: BC
37: CA (4 were AC)

ABCA   Approvals: C37,   B32,  A31
Now C doubly defeats A, and B wins. (AWP also elects B)

http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-October/023017.html


Chris Benham




Kevin Venzke wrote (Mon.Oct.20):
Hi Kristofer,

--- En date de : Lun 20.10.08, Kristofer Munsterhjelm km-elmet at 
broadpark.no a écrit :
You could also have the approval version of Smith,IRV. Call
it 
Condorcet,Approval. I think it's Smith (so it would be
Smith,Approval), 
but I'm not sure. The method is this: Drop candidates,
starting with the 
Approval loser and moving upwards, until there's a CW.
Then that one is 
the winner.

This method has been invented from scratch a few times; most recently
it was called Definite Majority Choice.

I don't think it can be described using double-slash or comma notation...

For instance Smith//FPP would mean that you eliminate all non-Smith
candidates and elect the FPP winner pretending that the eliminated
candidates never existed. Whereas Smith,FPP would mean that you elect
that Smith candidate who had the most first preferences to start with.

When Condorcet is the first or Approval is the second component, it's
not likely to make a difference which punctuation is used.

Is Condorcet,Approval (Smith,Approval?) nonmonotonic? If
not, and it is 
Smith, then you have a simple Smith-compliant
Condorcet/approval method.

It satisfies Smith and monotonicity.

Kevin Venzke


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[EM] Re : About Condorcet//Approval

[Chris Benham]

Kevin,
I've always thought that the main value of  mono-raise is that methods that 
fail it are 
vulnerable to Pushover strategy and those that meet it aren't. 

push-over 
The strategy of ranking a weak alternative higher than one's preferred 
alternative, which may be useful in a method that violates monotonicity.
http://condorcet.org/emr/defn.shtml

But now you are proposing an interpretation of  mono-raise (aka monotonicity) 
that can 
be met by a method that is clearly vulnerable to Pushover strategy.
 
25: AB
26: BC
23: CA
26: C

What is the value/use of a criterion that does that and moreover can be met by 
a method
that fails to elect C in the above election?   
 
The method under discussion that you say meets mono-raise, Definite Majority 
Choice
(Whole), elects B.
 
 
All candidates are in the top cycle, but by our 3-slot ratings ballot 
interpretation C has
the highest TR score, the highest  approval score, and the lowest 
approval-opposition
score.
 
Would you agree then that there is a need for an  Invulnerability to Pushover 
strategy
criterion, that is more important than mono-raise?
 
Chris Benham
 

 

Hi Chris,

--- En date de : Jeu 23.10.08, Chris Benham cbenhamau at yahoo.com.au a 
écrit :
Kevin,
I think the version of  DMC  that allows voters to rank among unapproved
candidates fails mono-raise, and both versions are vulnerable to Pushover
strategy. 

Would you say that that the plain all ranked are
approved version doesn't properly fail mono-raise but instead fails
mono-raise-delete?

I think it definitely fails the latter. I think it only fails the former
if you can't rank all the candidates (for approval purposes).

http://lists.electorama.com/pipermail/election-methods-electorama.com/2007-March/019824.html

I wrote in March 2007:
With the approval cutoffs, DMC  (and AWP) come close to
failing mono-raise.

31: AB
04: AC
32: BC
33: CA

ABCA   Approvals: A35,  B32,   C33. 
A eliminates (doubly defeats) B, and C wins. (AWP measures 
defeat-strengths by the number of ballots on the winning
side that approve the 
winner and not the loser, and so says C's defeat is the
weakest and so also
elects C.)

Now change the 4 AC ballots to CA

To my mind you aren't allowed to move C over both A and the cutoff at
the same time, unless the method for some reason doesn't allow it any
other way (such as if this is the bottom of the ballot and you can't
approve all candidates).

Kevin Venzke

I misstated something:

--- En date de : Dim 26.10.08, Kevin Venzke stepjak at yahoo.fr a écrit :
 Now change the 4 AC ballots to CA

To my mind you aren't allowed to move C over both A and
the cutoff at
the same time, unless the method for some reason
doesn't allow it any
other way (such as if this is the bottom of the ballot and
you can't
approve all candidates).

You can move C over both at the same time, but you can't, at this same
time, move A and the cutoff relative to each other, according to my
opinion.

Kevin Venzke


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Re: [EM] In defense of the Electoral College (was Re: Making a Bad Thing Worse)

[Chris Benham]

Steve Eppley wrote (Th. Nov.6):
Hi,

Greg Nisbet wrote on 10/18/08:
-snip-
The Electoral College:
This is generally regarded as a bad thing. No one really appears to
support it except as an adhoc version of asset voting.
-snip-

I don't believe the EC is generally accepted as a bad thing. (I picked 
the Subject line above to cite a book by the same name.)  Although I may 
have been the person who came up with the idea for how to get rid of the 
EC without a constitutional amendment (posted in EM many years ago), I 
later concluded the EC is better than a national popular vote.
-snip-

One widespread argument against the EC is that it flouts the commonsense
fairness axiom that all votes should be weighted equally.

A national popular vote would exacerbate polarization, since candidates 
could/would focus on voter turnout of their base instead of having to 
appeal to swing voters in a few close states.

I don't see how preventing the supposed evil of  exacerbating polarisation
anything like justifiies the unfairness evil of weighting votes unequally.

And in any case I don't accept the argument. Why wouldn't candidates
have incentive to appeal to swing voters  *across the whole country*??

Why would anyone go to the trouble of elaborating and proposing a 
relatively complicated ranked-ballot method that is justified by meeting
the Condorcet criterion and Majority for Solid Coalitions and so on,
and then turn around and suggest that it is desirable that weighting votes
unequally should be maintained, thus ensuring that any voting method
cannot meet those criteria or even  Majority Favourite or Majority
Loser?

A national popular vote would exacerbate the candidates' need for 
campaign money, since they would not be able to focus on the few states 
that are close.  That would make them more beholden to wealthy special 
interests.

A national popular vote would make for a nightmare when recounting a 
close election.  The recounting wouldn't be confined to a few close states.

Plenty of other countries directly elect their presidents without any EC,
and yet it is the US that has these problems (more severely).

I think the counting problems would be less likely with a national popular
vote, simply because it is very unlikely to be very close. The scenario
that it is very close in some (using the the EC)  critical states but not
close in the overall popular vote is much more likely than it being very
close in both.

 
Chris Benham


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[EM] New MN court affidavits by those defending non-Monotonic voting methods IRV/STV

[Chris Benham]

Greg wrote (Th.Nov.6):
Those documents make a good case. If you rule IRV/STV unconstitutional
due to non-monotonicity, you have to be prepared to rule open
primaries and top-two primaries unconstitutional as well.

Note also that other arguments by the MN Voter's Alliance would, if
successful, would render *any* voting method that involves putting
marks next to multiple candidates -- IRV, Bucklin, Approval,
Condorcet, Range -- by its nature unconstitutional.

-snip-

That anti-IRV group explicitly say as much:

Additional note:  There are several other non-traditional voting methods 
currently being advocated around the country. Among these are Range Voting
and Approval Voting. (See the NYU report linked above) While these schemes
are better in some ways than IRV, they retain some of the same fatal flaws which
 make IRV unconstitutional.

http://www.mnvoters.org/IRV.htm


Chris Benham



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[EM] In defense of the Electoral College (was Re: Making a Bad Thing Worse)

[Chris Benham]

Kevin Venzke wrote (Fri.Nov.7):
Hi,

--- En date de : Ven 7.11.08, Markus Schulze markus.schulze at 
alumni.tu-berlin.de a écrit :
Second: It makes it possible that the elections
are run by the governments of the individual
states and don't have to be run by the central
government.

I especially agree with this second point, or at least that it has been
a good thing that the elections have not been conducted by a single
authority.

It's possible to imagine a different American history, if the federal
government had been in a position to cancel or postpone or manipulate the 
presidential election.

Kevin Venzke

 
Kevin,
Why does having elections for national office run by a central authority
like a federal electoral commission  necessarily mean that the federal
government (presumably you refer here to partisan office-holders with
a stake in the election outcome) would have the power to cancel or
postpone or manipulate the presidential election?

Can you please support your point by comparing the US with other
First World countries, perhaps just focussing on the last few decades?

Chris Benham



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[EM] New MN court affidavits by those defending non-Monotonic voting methods IRV/STV

[Chris Benham]

Dave,
Are you really comfortable supporting and supplying ammunition to a 
group of avowed FPP supporters in their effort to have IRV declared
unconstitutional?

Will have any complaint when in future they are trying to do the same
thing to some Condorcet method you like and IRV supporters help
them on grounds like it fails Later-no-Harm, Later-no-Help, and 
probably  mono-add-top?

Chris Benham

 



Dave Ketchum wrote (Fri.Nov.7):
Perhaps this could get some useful muscle by adding such as:
  9 BA

Now we have 34 voting BA.  Enough that they can expect to win and may have 
as strong a preference between these two as might happen anywhere.

C and D represent issues many feel strongly about - and can want to assert 
to encourage action by B, the expected winner.  If ONE voter had voted BA 
rather than DBA, IRV would have declared B the winner.

Note that Condorcet would have declared B the winner any time the BA count 
exceeded the AB count (unless C or D got many more votes).

DWK

On Fri, 7 Nov 2008 14:05:03 -0700 Kathy Dopp wrote:
Dave,

I agree with you -that is important too, but the attorneys and
judge(s) have their own criteria for judging importance as compared to
existing laws.

Your example IMO does show unequal treatment of voters, so perhaps
I'll include it as one of many ways to show how IRV unequally treats
voters and see if the attorneys use it or not.

Thanks.

Kathy


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[EM] Why I Prefer IRV to Condorcet

[Chris Benham]

Greg,
I generally liked your essay. I rate IRV as the best of the single-winner 
methods that
meet Later-no-Harm, and a good method (and a vast improvement on FPP).

But I think you made a couple of technical errors.

However, because bullet voting can help and never backfire against one's top 
choice under
Condorcet, expect every campaign with a shot at winning to encourage its 
supporters to 
bullet vote. 

Bullet voting can backfire against one's top choice under Condorcet because 
Condorcet
methods, unlike IRV, fail Later-no-Help. 

http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf

In this 1996 Douglas Woodall paper, see Election 6 and the accompanying 
discussion on
page 5/6 of the pdf (labelled on the paper as Page 13).

Quoting again from your paper:
As mentioned, every voting system is theoretically vulnerable to strategic 
manipulation, and IRV 
is no exception. However, under IRV, there is no strategy that can increase the 
likelihood of 
electing one's first choice beyond the opportunity offered by honest rankings. 
While there are 
strategies for increasing the chances of less preferred candidates under IRV, 
like push-over, 
they are counter-intuitive.

The Push-over strategy is certainly not limited to improving the chance of 
electing a lower 
[than first] choice. Say sincere is:

49: A 
27: BA
24: CB

B is the IRV winner, but if  4-21 (inclusive) of the A voters change to C or 
C? then the winner
changes to A.

But as you say the strategy isn't intuitive , and backfires if too many of 
the A supporters try it.
Some IRV opponents claim to like Top-Two Runoff, but that is more vulnerable to 
Push-over 
than IRV (because the strategists can support their sincere favourite in the 
second round).

The quite intuitive strategy that IRV is vulnerable to is Compromise, like any 
other method that
meets Majority. But voters' incentive to compromise (vote one's front-runner 
lesser-evil in first
place to reduce the chance of front-runner greater-evil winning) is generally 
vastly vastly less
than it is under FPP.

(There are methods that meet both Majority and Favourite Betrayal, and in them 
compromisers
can harmlessly vote their sincere favourites in equal-first place.)

But some Condorcet advocates are galled  by the Compromise incentive that can 
exist where
there is a sincere CW who is not also a sincere Mutual Dominant Third winner.

49: AB
02: BA
22: B
27: CB

On these votes B is the CW, but IRV elects A.  If the CB voters change to B 
then B will be 
the voted majority favourite, so of course IRV like Condorcet methods and FPP 
will elect B.

Chris Benham

 
Greg wrote (Wed.Nov.19, 2008):
I have written up my reasons for preferring IRV over Condorcet methods
in an essay, the current draft of which is available here:
  http://www.gregdennis.com/voting/irv_vs_condorcet.html

I welcome any comments you have.

Thanks,
Greg



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[EM] Unmanipulable Majority strategy criterion

[Chris Benham]

I have a suggestion for a new strategy criterion I might call  
Unmanipulable Majority.

*If (assuming there are more than two candidates) the ballot 
rules don't constrain voters to expressing fewer than three 
preference-levels, and A wins being voted above B on more 
than half the ballots, then it must not be possible to make B 
the winner by altering any of the ballots on which B is voted 
above A.*

Does anyone else think that this is highly desirable?

Is it new?

Chris Benham


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[EM] Why I think IRV isn't a serious alternative

[Chris Benham]

Forest,
Given IRV's compliance with the representativeness criteria Mutual Dominant 
Third, Majority for
Solid Coalitions, Condorcet Loser and  Plurality; why should the bad look of  
its erratic behaviour
be sufficient to condemn IRV in spite of these and other positive criterion 
compliances such as
Later-no-Harm and  Burial Invulnerability?

in the best of all possible worlds, namely normally distributed voting 
populations in no more 
than two dimensional issue space.

Why does that situation you refer to qualify as the best of all possible 
worlds ?

Chris  Benham



Forrest Simmons wrote  (Wed. Nov.26):
Greg,

When someone asks for examples of IRV not working well in practice, they are 
usually protesting against 
contrived examples of IRV's failures.  Sure any method can be made to look 
ridiculous by some unlikely 
contrived scenario.

I used to sympathize with that point of view until I started playing around 
with examples that seemed natural 
to me, and found that IRV's erratic behavior was fairly robust.  You could vary 
the parameters quite a bit 
without shaking the bad behavior.

But I didn't expect anybody but fellow mathematicians to be able to appreciate 
how generic the pathological 
behavior was, until ...

... until the advent of the Ka-Ping Lee and B. Olson diagrams, which show 
graphically the extent of the 
pathology even in the best of all possible worlds, namely normally distributed 
voting populations in no more 
than two dimensional issue space.

These diagrams are not based upon contrived examples, but upon 
benefit-of-a-doubt assumptions.  Even 
Borda looks good in these diagrams because voters are assumed to vote sincerely.

Each diagram represents thousands of elections decided by normally distributed 
sincere voters.

I cannot believe that anybody who supports IRV really understands these 
diagrams.  Admittedly, it takes 
some effort to understand exactly what they represent, and I regret that the 
accompaning explanations are 
too abstract for the mathematically naive.  They are a subtle way of displaying 
an immense amount of 
information.

One way to make more concrete sense out of these diagrams is to pretend that 
each of the candidate 
dots actually represents a proposed building site, and that the purpose of each 
simulated election is to 
choose the site from among these options.

Each of the other pixels in the diagram represents (by its color) the outcome 
the election would have (under 
the given method) if a normal distribution of voters were centered at that 
pixel.

So each pixel of the diagram represents a different election, but with the same 
candidates (i.e. proposed 
construction sites).

Different digrams explore the effect of moving the candidates around relative 
to each other, as well as 
increasing the number of candidates.

With a little practice you can get a good feel for what each diagram 
represents, and what it says about the 
method it is pointed at (as a kind of electo-scope).

On result is that IRV shows erratic behavior even in those diagrams where every 
pixel represents an election 
in which there is a Condorcet candidate.

My Best,

Forest


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[EM] Unmanipulable Majority strategy criterion

[Chris Benham]

Kristofer,

...your Dominant Mutual Quarter Burial Resistance property.

I don't  remember reading or hearing about anything like that with Quarter in 
the title
anywhere except in your EM  posts. 

A few years ago  James Green-Armytage coined the Mutual Dominant Third 
criterion
but never promoted it.  I took it up, but sometimes mistakenly reversed the 
order of the first 
two words. I now think the original order is better, because MDT is analogous 
with the 
better-known older Mutual Majority criterion.

I do remember suggesting  what is in effect MDT Burial Resistance, because 
there is an
ok method that meets it while failing Burial Invulnerability: namely Smith,IRV.

I don't know of any method that meets  the MDQBR you refer to that isn't 
completely in
invulnerable to Burial (do you?), so I don't see how that criterion is 
presently useful.

In response to my question is Unmanipulative Majority desirable?  you wrote:

In isolation (not affecting anything else), sure. It's desirable because  it 
limits the burying 
tricks that can be done.

I'm glad you think so.

The mention of pushover strategy there would mean that the method would 
have to have some degree of monotonicity, I assume.

Yes.

If AX voters can cause A to win by rearranging  their ballots, then that 
would be a 
form of constructive burial. If, for instance, some subset of the voters who 
place X 
fifth can keep X from winning by rearranging their first-to-fourth preferences, 
then that 
would be destructive burial.

If those voters are sincere in ranking X fifth, i.e they sincerely prefer all 
the candidates
they rank above X to X; then I can't see that that qualifies as Burial 
strategy at all.

Normally the strategy you refer to would qualify as some form of  Compromise 
strategy.
(Do you have an example that doesn't?)

Chris Benham





Kristofer Munsterhjelm wrote (Fri.Nov.28) wrote:

Chris Benham wrote:
  
 Kristofer,
 Thanks for at least responding.
  
 ...I won't say anything about the desirability because I  don't know 
 what it implies;..
 
 Only judging criteria by how they fit in with other criteria is 
 obviously circular.

That's true. If we're going to judge criteria by how they fit in with 
other criteria, we should have an idea of how relatively desirable they are.

It may also be the case that it the tradeoff would be too great, by 
reasoning similar to what I gave in the reply to Juho about your 
Dominant Mutual Quarter Burial Resistance property. But if we consider 
this in more detail, we don't really know whether such tradeoffs are too 
great for, for instance, cloneproof criteria (though I think they are not).

 Do you (or anyone) think that judged in isolation this strategy 
 criterion is desirable?
 It is true that some desirable/interesting criteria are so restrictive 
 (as you put it) that
 IMO  compliance with them can only be a redeeming feature of  a method 
 that isn't
 one of the best.  (I  put Participation in that category.)

In isolation (not affecting anything else), sure. It's desirable because 
it limits the burying tricks that can be done.

If you're asking whether I think it's more important than being, say, 
cloneproof, I don't think I can answer at the moment. I haven't thought 
about the relative desirability of criteria, though I prefer Condorcet 
methods to be both Smith and cloneproof.

 Maybe some people would like me to paraphrase this suggested criterion 
 in language
 that is more EM-typical:
 
 'If candidate A majority-strength pairwise beats candidate B, then it 
 must not be possible for B's
 supporters (pairwise versus A) to use Burial or Pushover strategy to 
 change the winner from A
 to B.'

The mention of pushover strategy there would mean that the method would 
have to have some degree of monotonicity, I assume.

 Destructive burial would be trying to make X not win,...
  
 Your destructive burial  looks  almost synonymous with *monotonicity*.

Hm, not necessarily. Without qualifications on the criterion, 
destructive burial would be constructive burial for *any* candidate, but 
also more than that. If AX voters can cause A to win by rearranging 
their ballots, then that would be a form of constructive burial. If, for 
instance, some subset of the voters who place X fifth can keep X from 
winning by rearranging their first-to-fourth preferences, then that 
would be destructive burial.



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[EM] Unmanipulable Majority strategy criterion definition amended

[Chris Benham]

I propose to amend my suggested  Unmanipulable Majority
criterion by simply adding a phrase beginning with without.. 
so that it now reads:

*If (assuming there are more than two candidates) the ballot 
rules don't constrain voters to expressing fewer than three 
preference-levels, and A wins being voted above B on more 
than half the ballots, then it must not be possible to make B 
the winner by altering any of the ballots on which B is voted 
above A without raising their ranking or rating of B.*

(Later I might rephrase it just to make it more succinct and
polished).

The effect of  the alteration is to preclude Compromise strategy.
When I first suggested the original version I knew that many methods
fail it due to Burial and/or  Push-over, but I mistakenly thought that
my recent 3-slot method suggestion (defined below) meets it.


*Voters fill out 3-slot ratings ballots, default rating is bottom-most
(indicating least preferred and not approved).

Interpreting top and middle rating as approval, disqualify all candidates
with an approval score lower than their maximum approval-opposition (MAO) 
score.
(X's  MAO score is the approval score of the most approved candidate on
ballots that don't approve X).

Elect the undisqualified candidate with the highest top-ratings score.*

My preferred name for that method is now Strong Minimal Defense, Top
Ratings (SMD,TR). 

45: A
03: AB
47: BA
02: XB
03: YA

Approvals:   A98,  B52,  Y3,   X2
Max. AO:    A2,    B48,  Y95, X95
Top Ratings: A48, B47,   Y3,  X2.

X and Y are disqualified, and  A wins.

A  is voted above B on more than half the ballots, but if all the ballots on
which B is voted above A are altered so that they all plump for B (top-rate B
and approve no other candidates) then B wins.


45: A
03: AB
49: B 
03: YA

Approvals:   A51,  B52,  Y3,   X0
Max. AO:    A49,  B48,  Y52, X52
Top Ratings: A48, B49,   Y3,  X0

As before only X and Y are disqualified, but now B has the highest Top Ratings
score.

I will soon post more on the subject of  which methods meet or fail the (newly
amended)  Unmanipulable Majority criterion.

Chris Benham


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[EM] Why I think IRV isn't a serious alternative

[Chris Benham]

Forest,
What nicer distribution can  you think of..

Nice (and nicer) is a fuzzy emotional/aesthetic term that I might apply to 
food, music, people etc.
but seems unscientific and out-of-place here (and I'm not sure exactly what 
it's supposed to mean). 

I can see that such a distribution is more comfortable for methods that try to 
elect the centrist candidate.

I see IRV as FPP that trades most of its monotonicity criteria (including 
mono-raise and Participation but 
not mono-add-top, mono-add-plump or mono-append) to gain Clone-Winner and 
Majority for Solid
Coalitions (and Mutual Dominat Third and Condorcet Loser).

It keeps FPP's compliances with Woodall's Plurality criterion, Later-no-Harm, 
Later-no-Help and Clone-Loser.

The representativeness criteria it meets generally allow for a bigger set of 
allowable winners than say
the Smith set, and its monotonity failures mean that it chooses a winner from 
this set a bit erratically.
But I think your use of  the term pathology (comparing it to a disease and so 
something  that is self-evidently
unacceptable) is biased and out of place.

I also think that the argument that IRV makes a good stepping-stone to  PR is 
strong. Truly proportional 
multi-winner methods meet  Droop Proportionality for Solid Coalitions 
(equivalent in the single-winner 
case to Majority for Solid Coalitions, aka Mutual Majority.)

Single-winner STV's  virtues of  Later-no-Harm and Clone Independence survive 
into the multi-winner 
version (which of course meets Droop Proportionality SC), while for 
multi-winner methods the Condorcet 
criterion and Favourite Betrayal  are both incompatible with Droop PSC.  Also I 
think Later-no-Harm 
compliance is more valuable for multi-winner methods than for single-winner 
methods.

Chris Benham



Forest Simmons wrote (Sat. Nov.29):

From: Chris Benham 
  Forest,
 Given IRV's compliance with the representativeness criteria  Mutual 
 Dominant Third, Majority for
 Solid Coalitions, Condorcet Loser and? Plurality; why should the  bad look of 
 its erratic behaviour
 be sufficient to condemn IRV in spite of these and other  positive criterion 
 compliances such as
 Later-no-Harm and Burial Invulnerability?
 
A picture is worth a thousand words.  It shows the actual behavior, including 
the extent of the pathology.

  in the best of all possible worlds, namely normally distributed voting 
  populations in no more 
 than two dimensional issue space.
 CB: Why does that situation you refer to qualify as the best of all  
 possible worlds ?
 Three points determine a plane, so we cannot expect a lower dimension than 
 two. What nicer 
distribution can you think of. than normal?  But any distribution whose 
density only depends on distance 
from the center of the distribution would give exactly the same results for 
any Condorcet method, without 
making the IRV results any nicer. 

Forest


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[EM] Unmanipulable Majority strategy criterion (newly amended version)

[Chris Benham]

Regarding my proposed Unmanipulable Majority criterion:

*If (assuming there are more than two candidates) the ballot 
rules don't constrain voters to expressing fewer than three 
preference-levels, and A wins being voted above B on more 
than half the ballots, then it must not be possible to make B 
the winner by altering any of the ballots on which B is voted 
above A without raising their ranking or rating of B.*

To have any point a criterion must be met by some method.

It is met by my recently proposed SMD,TR method, which I introduced
as 3-slot SMD,FPP(w):

*Voters fill out 3-slot ratings ballots, default rating is bottom-most
(indicating least preferred and not approved).

Interpreting top and middle rating as approval, disqualify all candidates
with an approval score lower than their maximum approval-opposition 
(MAO) score.
(X's  MAO score is the approval score of the most approved candidate on
ballots that don't approve X).

Elect the undisqualified candidate with the highest top-ratings score.*

Referring to the UM criterion: (a) if candidate A has a higher TR score than B
then the BA strategists can only make B win by causing A to be disqualified.
But in this method it isn't possible to vote x above y without approving x, so
we know that just on the AB ballots A has majority approval. It isn't possible
for a majority-approved candidate to be disqualified, and the strategists can't
cause A's approval to fall below majority-strength. And the criterion specifies
that none of the BA voters who don't top-rate B can raise their rating of B to
increase B's TR score.

(b) if on the other hand B has a higher TR score than A but B is disqualified
there is nothing the BA strategists can do to undisqualify B.

So SMD,TR meets the UM criterion.

93: A
09: BA
78: B
14: CB
02: CA
04: C
200 ballots

BA  101-95,  BC 87-20,  AC 102-20.
All Condorcet methods, plus MDD,X  and  MAMPO and  ICA elect B.

B has a majority-strength pairwise win against A, but say 82 of the 93A change 
to
AC  thus:

82: AC
11: A
09: BA
78: B
14: CB
02: CA
04: C

BA  101-95,  CB 102-87,  AC 102-20
Approvals: A104, B101, C102
TR scores: A93,   B87,   C 20

Now MDD,A and MDD,TR and MAMPO and ICA and  Schulze/RP/MinMax etc. using 
WV or Margins elect A.  So all those methods fail the UM criterion.

25: AB
26: BC
23: CA
26: C

BC 51-49,   CA 75-25,  AB 48-26

Schulze/RP/MM/River (WV) and Approval-Weighted Pairwise and DMC and MinMax(PO)
and MAMPO and IRV elect B.

Now say 4 of the 26C change to AC (trying a Push-over strategy):


25: AB
04: AC
26: BC
23: CA
22: C

BC 51-49,   CA 71-29,  AB 52-26

Now Schulze/RP/MM/River (WV) and  AWP and DMC and MinMax(PO) and MAMPO
and IRV all elect C. Since B had/has a majority-strength pairwise win against 
C, all these
methods also fail  Unmanipulable Majority. If  scoring ballots were used and 
all voters score
their most preferred candidate 10 and any second-ranked candidate 5 and 
unranked candidates
zero, then this demonstration also works for IRNR so it also fails.

Who knew that such vaunted  monotonic methods as WV and  MinMax(PO) and MAMPO
were vulnerable to Push-over?!

48: AB
01: A
03: BA
48: CB

BA 51-49.  Bucklin and MCA elect B, but if the 48 AB voters truncate the 
winner changes
to A.  So those methods also fail UM.

49: A9, B8, C0
24: B9, A0, C0
27: C9, B8, A0

Here Range/Average Ratings/Score/CR elects B and on more than half the ballots 
B is voted 
above A, but if  the 49 A9, B8, C0 voters change to  A9, B0, C0  the winner 
changes to A.
So this method fails UM.

48: ABCD
44: BADC
04: CBDA
03: DBCA

Here Borda elects B and B is voted above A on more than half the ballots, but 
if the 48 
ABCD ballots are changed to ACDB the  Borda winner changes to A, so
Borda fails UM.

This  Unmanipulable Majority criterion is failed by all well known and 
currently advocated
methods, except  3-slot SMD,TR!

Given its other criterion compliances and simplicity, that is my favourite 
3-slot s-w method
and my favourite Favourite Betrayal complying method.


Chris Benham


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[EM] Unmanipulable Majority strategy criterion

[Chris Benham]

Kristofer,
You wrote addressing me:
You have some examples showing that RP/Schulze/etc fail the criterion.

By my lazy etc. I just meant  'and the other Condorcet methods that are 
all equivalent to MinMax when there are just 3 candidates and Smith//Minmax
when there are not more than 3 candidates in the Smith set'.

Do they show that Condorcet and UM is incompatible? Or have they just 
been constructed on basis of some Condorcet methods, with differing 
methods for each?

My intention was to show that all the methods that take account of more than 
one possible voter preference-level (i.e. not Approval or FPP) (and are 
well-known and/or advocated by anyone on EM) are vulnerable to UM except 
SMD,TP.

I think I remember that you said Condorcet implies some vulnerability to 
burial. Is that sufficient to make it fail UM?

Probably yes, but I haven't  tried to prove as much. 

Returning to this demonstration:


93: A
09: BA
78: B
14: CB
02: CA
04: C
200 ballots

BA  101-95,  BC 87-20,  AC 102-20.
All Condorcet methods, plus MDD,X  and  MAMPO and  ICA elect B.

B has a majority-strength pairwise win against A, but say 82 of the 93A change 
to
AC  thus:

82: AC
11: A
09: BA
78: B
14: CB
02: CA
04: C

BA  101-95,  CB 102-87,  AC 102-20
Approvals: A104, B101, C102
TR scores: A93,   B87,   C 20

Now MDD,A and MDD,TR and MAMPO and ICA and  Schulze/RP/MinMax etc. using 
WV or Margins elect A.  So all those methods fail the UM criterion.

Working in exactly the same way as ICA (because no ballots have voted more than 
one candidate
top), this also applies to  Condorcet//Approval and Smith//Approval and 
Schwartz//Approval.
So those methods also fail UM.

I did a bit of calculation and it seems my FPC (first preference 
Copeland) variant elects B here, as should plain FPC. Since it's 
nonmonotonic, it's vulnerable to Pushover, though, and I'm not sure 
whether that can be fixed at all.

My impression is/was that in 3-candidates-in-a-cycle examples that method 
behaves just like IRV.
The demonstration that I gave of  IRV failing UM certainly also applies to it. 


Chris Benham



Kristofer Munsterhjelm  wrote (Thurs.Dec.4):
Chris Benham wrote:
Regarding my proposed Unmanipulable Majority criterion:
  
*If (assuming there are more than two candidates) the ballot
rules don't constrain voters to expressing fewer than three
preference-levels, and A wins being voted above B on more
than half the ballots, then it must not be possible to make Bthe winner by 
altering any of the ballots on which B is voted
above A without raising their ranking or rating of B.*
  
To have any point a criterion must be met by some method.
  
It is met by my recently proposed SMD,TR method, which I introduced
as 3-slot SMD,FPP(w):

*Voters fill out 3-slot ratings ballots, default rating is bottom-most
(indicating least preferred and not approved).

Interpreting top and middle rating as approval, disqualify all candidates
with an approval score lower than their maximum approval-opposition
(MAO) score.
(X's  MAO score is the approval score of the most approved candidate on
ballots that don't approve X).

Elect the undisqualified candidate with the highest top-ratings score.*
  
[snip examples of methods failing the criterion]

You have some examples showing that RP/Schulze/etc fail the criterion. 
Do they show that Condorcet and UM is incompatible? Or have they just 
been constructed on basis of some Condorcet methods, with differing 
methods for each?

I think I remember that you said Condorcet implies some vulnerability to 
burial. Is that sufficient to make it fail UM? I wouldn't be surprised 
if it is, seeing that you have examples for a very broad range of 
election methods.

93: A
09: BA
78: B
14: CB
02: CA
04: C
200 ballots

BA  101-95,  BC 87-20,  AC 102-20.
All Condorcet methods, plus MDD,X  and  MAMPO and  ICA elect B.

B has a majority-strength pairwise win against A, but say 82 of the 93A 
change to
AC  thus:

82: AC
11: A
09: BA
78: B
14: CB
02: CA
04: C
  
BA  101-95,  CB 102-87,  AC 102-20
Approvals: A104, B101, C102
TR scores: A93,   B87,   C 20
  
Now MDD,A and MDD,TR and MAMPO and ICA and  Schulze/RP/MinMax etc. using
WV or Margins elect A.  So all those methods fail the UM criterion.

I did a bit of calculation and it seems my FPC (first preference 
Copeland) variant elects B here, as should plain FPC. Since it's 
nonmonotonic, it's vulnerable to Pushover, though, and I'm not sure 
whether that can be fixed at all.



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[EM] IRV's Squeeze Feature

[Chris Benham]

Forest,
You wrote, setting up your attack on IRV:
Suppose that the voters are distributed uniformly on a disc with center C, and 
that they are voting to 
choose from among several locations for a community center.

(a) That is quite a big suppose, and  (b) I agree that IRV would not be among 
the best methods
to use to vote to choose the location of a community centre.

The center C of any distribution of voters with central symmetry through C 
will be a Universal Condorcet 
Option for that distribution.

Yes, that is almost a tautology (and to the extent that it isn't it seems to 
be just a semantic point).

And what justification for winning does the IRV winner have?

I agree that if we suddenly have unfettered access to all the voters' sincere 
pairwise preferences and that
each voter's different pairwise preferences are all at least approximately as 
strong as each other, then yes
electing the Condorcet winner is nicer and philosophically more justified 
than electing the IRV winner. 

However the IRV winner could have as its justification simply the criterion 
compliances of the IRV method.
You, as the election-method salesman, could say to the polity/voters  
'customer':
This Condorcet method is definitely best for choosing the most central 
community centre with sincere voting. 
I recommend it. 

but they could reply: 
Does it meet Burial Invulnerability and Later-no-Harm and Later-no-Help as 
well as Mutual Dominant Third 
and Mutual Majority and  Condorcet Loser and Woodall's Plurality criterion and 
Clone Independence?

To which you must reply No, and then the 'customer' says Then which is the 
best method that does?, to
which you reply IRV and make the sale.

IRV has some more-or-less unique problems but they are the unavoidable price 
of  a unique set of  strengths,
so I don't consider it justified to focus on its problems in isolation. Often 
this is done, comparing (sometimes
implicitly) IRV with the best features of several other methods. 

But as you know, I am also supportively interested in Condorcet methods and 
also Favourite Betrayal 
complying methods such as 3-slot SDC,TR.

Chris Benham



Forest Simmons wrote (Fri. Dec.5):
Suppose that the voters are distributed uniformly on a disc with center C, and 
that they are voting to 
choose from among several locations for a community center.

Then no matter how many locations on the ballot, if the voters rank them from 
nearest to furthest, the 
location nearest to C will be the Condorcet Option.

Therefore, if C itself is one of the options, it will be the Condorcet Option 
no matter what the other 
options are.  So C is more than just a regular run of the mill Condorcet 
Option, it is a kind of Universal 
Condorcet Option for this distribution of voters.

The center C of any distribution of voters with central symmetry through C will 
be a Universal Condorcet 
Option for that distribution.

But no matter how peaked that distribution might be (even like the roof of a 
Japanese pagoda) the center 
C is not immune from the old IRV squeeze play.

If the good and bad cop team gangs up on C, one on each side, they can reduce 
C's first choice region 
to a narrow band perpendicular to the line connecting the two team mates, thus 
forcing C out in the first 
round of the runoff.

If the team mates are not perfectly coordinated, then instead of a narrow band, 
C's first choice region 
becomes a long narrow pie piece shaped wedge, roughly perpendicular to the line 
determined by the two 
team mates.

This squeeze play can be used against any candidate no matter the shape of the 
distribution, symmetric 
or not.  But my point is that even in a sharply peaked unimodal symetrical 
distribution, the center C, 
which is the Universal Condorcet Option, can easily be squeezed out under IRV.  
And what justification 
for winning does the IRV winner have?  Merely that it was the closer of the two 
team mates to the ideal 
location C.

Now leaving the concrete setting of voting for a physical location for a 
community center, and getting 
back to a more abstract political issue space: It doesn't really matter if the 
good cop and bad cop are 
really even anywhere near to opposite sides of a targeted candidate (say a 
strong third party challenger) 
as long as they can make it appear that way.

The two corporate parties are very good at this good cop / bad cop game, 
especially since the major 
media manipulators of public opinion are completely beholden to the giant 
corporations.


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[EM] Why I Prefer IRV to Condorcet

[Chris Benham]

Kristofer,

You wrote (Sun.Nov.23):
Regarding number two, simple Condorcet methods exist. Borda-elimination 
(Nanson or Raynaud) is Condorcet. Minmax is quite simple, and everybody 
who's dealt with sports knows Copeland (with Minmax tiebreaks). I'll 
partially grant this, though, since the good methods are complex, but 
I'll ask whether you think MAM (Ranked Pairs(wv)) is too complex. In 
MAM, you take all the pairwise contests, sort by strength, and affirm 
down the list unless you would contradict an earlier affirmed contest. 
This method is cloneproof, monotonic, etc...

Raynaud isn't  Borda-elimination.  It is  Pairwise Elimination, i.e. eliminate
the loser of  the most decisive or strongest pairwise result (by one measure or
another) until one candidate remains.  You may have instead meant to write 
Baldwin,though some sources just talk about 2 different versions of  Nanson.

Simpler and much better than any of those methods are  Condorcet//Approval
and  Smith//Approval and  Schwartz//Approval ,in each case interpreting 
ranking as approval and so not allowing ranking among unapproved candidates.

Chris Benham


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[EM] Unmanipulable Majority strategy criterion (Kristofer)

[Chris Benham]

Kristofer Munsterhjelm wrote (Sat.Nov.29):

-snip-

I don't know of any method that meets  the MDQBR you refer to that isn't 
completely invulnerable to Burial (do you?), so I don't see how that criterion 
is 
presently useful.

That's odd, because the example I gave in a reply to Juho was yours.
http://listas.apesol.org/pipermail/election-methods-electorama.com/2006-December/019097.html

Note that the method of that post (which I've been referring to as first 
preference Copeland) ...

-snip-

Kristofer,
Yes,sorry, that was a not-well-considered posting of mine that I'd forgotten.

That method, the basic version of which was introduced by Forest Simmons as 
Clone-proofed
Copeland, doesn't meet  Mutual Dominant Quarter Burial Resistance (MDQBR).

26: AB
25: CA
02: CB
25: BA
22: BC

AB 51-49,   AC 51-49,   BC  73-27.  

FPs: A26,  B47,  C27.  A is the CW and wins with the penalty score of  total 
FPs of candidates
pairwise beaten by of  zero. With over a quarter of the FPs A is a mutual 
dominant quarter 
candidate.

Say two of the 25 BA change to BC:

26: AB
25: CA
02: CB
23: BA
24: BC

AB 51-49,   CA 51-49,   BC  73-27

Now the penalty scores are  A27,  B26,  C47.  The Burial has worked, the new 
winner is B.

Chris Benham



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[EM] Push-over Invulnerability criterion

[Chris Benham]

Part of  my demonstration of  many methods' failure of the Unmanipulable 
Majority
criterion has inspired me to suggest another strategy criterion: 

Push-over Invulnerability:
*It must not be possible to change the winner from candidate X to candidate Y by
altering some ballots (that vote Y above both candidates  X and  Z) by raising 
Z above
Y without changing their relative rankings among other (besides X and Z) 
candidates.*

I might later suggest a more elegant re-wording, and/or suggest a simplified 
approximation
that is easier to test for.

25: AB
26: BC
23: CA
26: C

BC 51-49,   CA 75-25,  AB 48-26

Schulze/RP/MM/River (WV) and Approval-Weighted Pairwise and DMC and MinMax(PO)
and MAMPO and IRV elect B.

Now say 4 of the 26C change to AC (trying a Push-over strategy):

25: AB
04: AC
26: BC
23: CA
22: C

BC 51-49,   CA 71-29,  AB 52-26

Now Schulze/RP/MM/River (WV) and  AWP and DMC and MinMax(PO) and MAMPO
and IRV all elect C. 

For a long time I thought that only non-monotonic methods like IRV and  
Raynaud (that
fail mono-raise) were vulnerable to Push-over, so therefore there was no need 
for a separate
Push-over Invulnerability criterion.

But now we see that the Schulze, Ranked Pairs, MinMax, River algorithms (all 
equivalent with 3
candidates)  using Winning Votes are all vulnerable  to Push-over (as my 
suggested criterion
defines it).

Now I know that Winning Votes' failure can be seen as functionally really a 
failure of  Later-no-help,
because those C-supporting strategists could more safely achieve the same end 
just by changing
their votes from C to CA instead of from C to AC. But that is hardly a 
bragging point for WV.

I think this Pushover criterion  can be seen as a kind of  monotonicity 
criterion, in the sense that all
else being equal methods that meet it must be in some way more monotonic than 
those that don't.

I have shown that WV fails Pushover Invulnerability. I strongly suspect (but 
not at present up to
proving) that both Margins and  Schwartz//Approval (ranking) meet it.

Can anyone please give an example (or examples) that show that either or both 
of  Margins and
S//A(r)  fail my suggested Push-over Invulnerability criterion?

Chris Benham



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[EM] Why I think IRV isn't a serious alternative KD

[Chris Benham]

Kristofer,
Woodall's DAC and  DSC and  Bucklin and Woodall's similar QLTD
all meet mono-raise and Mutual Majority (aka Majority for Solid Coalitions).

DSC meets LNHarm and the rest meet LNHelp.

Chris Benham

 
Kristofer Munsterhjelm  wrote (Sun.Dec.21):
snip
In any case, it may be possible to have one of the LNHs and be monotonic 
and have mutual majority. I'm not sure, but perhaps (doesn't one of DAC 
or DSC do this?). If so, it would be possible to see (at least) whether 
people strategize in the direction of early truncation by looking at 
methods that fail LNHarm but pass LNHelp; that is, Bucklin.
snip


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[EM] CDTT criterion compliance desirable?

[Chris Benham]

Marcus,
You wrote (25 Dec. 2008):

Dear Chris Benham,

you wrote (25 Dec 2008):

I had already proposed this criterion in 1997.
Why then do you list it as Woodall's CDTT criterion
instead of your own Generalised Majority Criterion?

Did, as far as you know, Woodall ever actually proposethe CDTT criterion as 
something that is desirable for
methods to meet (instead of just defining the CDTT set)?

Woodall's main aims are to describe and to investigate
the different election methods. Compared to the
participants of this mailing list, Woodall is very
reluctant to say that some election method was good/bad
or that some property was desirable/undesirable.
 
That is true, but nonetheless the short answer to my second question
is 'no'. To quote  Douglas Woodall (with his permission) from a recent
email (19 Dec 2008):
 
I defined the CDTT set as a means towards constructing election methods 
with certain mathematical properties.  My memory for such things is not good, 
and I am open to correction, but as far as I recall I never suggested that for 
the 
winner to belong to the CDTT was particularly desirable, and I never suggested 
this as a criterion. So although calling it Woodall's CDTT criterion is an
understandable shorthand, it is somewhat misleading.

So can we agree that there isn't really such a thing as Woodall's CDTT 
criterion
and what you have  given that label to is your own Generalised Majority 
Criterion 
(GMC) that is equivalent to the winner must come from the  defined-by-Woodall
CDTT set?
 
I'm sorry if this seems excessively nitpicking, and I'm not suggesting you 
intended
to mislead with your understandable shorthand.
 
In my soon-to-follow next post I will explain why I think the GMC is a mistaken
standard.

Chris Benham


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[EM] GMC compliance a mistaken standard? (was CDTT criterion...)

[Chris Benham]

The  Generalised Majority Criterion says in effect that the winner
must come from Woodall's CDTT set, and is defined by Marcus Schulze
thus (October 1997):

Definition (Generalized Majority Criterion):

   X  Y means, that a majority of the voters prefers
   X to Y.

   There is a majority beat-path from X to Y, means,
   that X  Y or there is a set of candidates
   C[1], ..., C[n] with X  C[1]  ...  C[n]  Y.

   A method meets the Generalized Majority
   Criterion (GMC) if and only if:
   If there is a majority beat-path from A to B, but
   no majority beat-path from B to A, then B must not
   be elected.

With full strict ranking this implies Smith, and obviously 
Candidates permitted to win by GMC (i.e.CDTT), Random Candidate
is much better than plain Random Candidate. Nonetheless I think that compliance
with GMC is a mistaken standard in the sense that the best methods should
fail it.

The GMC concept is spectacularly vulnerable to Mono-add-Plump!

25: AB
26: BC
23: CA
04: C
78 ballots (majority threshold = 40)

BC 51-27,   CA 53-25,   AB 48-26.

All three candidates have a majority beat-path to each other, so GMC says that
any of them are allowed to win. 

But say we add 22 ballots that plump for C:

25: AB
26: BC
23: CA
26: C
100 ballots (majority threshold = 51)

BC 51-27,   CA 75-25,   AB 48-26.

Now B has majority beatpaths to each of the other candidates but neither of them
have one back to B, so the GMC says that now the winner must be B.

The GMC concept is also naturally vulnerable to Irrelevant Ballots. Suppose we 
now
add 3 new ballots that plump for an extra candidate X.

25: AB
26: BC 
23: CA
26: C
03: X
103 ballots (majority threshold = 52)

Now B no longer has a majority-strength beat-path to C, so now GMC says that C
(along with B) is allowed to win again.

(BTW this whole demonstration also applies to Majority-Defeat 
Disqualification(MDD)
and if we pretend that the C-plumping voters are trucating their sincere 
preference for B
over A then it also applies to Eppley's Truncation Resistance and Ossipoff's 
SFC and
GFSC criteria.)

If  the method uses 3-slot ratings ballots and we assume that the voted 3-slot 
ratings are
sincere, then the GMC can bar the plainly highest SU candidate from winning as 
evidenced
by its incompatibility with my recently suggested  Smith-Comprehensive 3-slot 
Ratings
Winner criterion:

*If no voter expresses more than three preference-levels and the ballot 
rules allow the expression of 3 preference-levels when there are 3 (or 
more) candidates, then (interpreting candidates that are voted above one
or more candidates and below none as top-rated, those voted above
one or more candidates but below all the top-rated candidates as 
middle-rated and those not voted above any other candidate and below
at least one other candidate as bottom-rated, and interpreting above-
bottom rating as approval) it must not be possible for candidate X to
win if there is some candidate Y which has a beat-path to X and  
simultaneously higher Top-Ratings and Approval scores and a lower  
Maximum Approval-Opposition score.*

http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023548.html

25: AB
26: BC 
23: CA
26: C

TR scores:  C49,   B26,    A25
App. scores:   C75,   B51,    A48
MAO scores: C25,   B49,A52

That criterion says that C  must win here. GMC says only B can win.

Frankly I think any method needs a much better excuse than any that Winning 
Votes
can offer for not electing C here. As I discuss in another recent post, any 
method
that doesn't elect C here must be vulnerable to Push-over. So another reason not
to be in love with GMC is that it is incompatible with Pushover 
Invulnerability.

http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023543.html

As I hope some may have guessed from the spectacular failure of Mono-add-Plump, 
the GMC 
concept is grossly unfair to truncators.  And Winning Votes  (as a GMC 
complying method) is
unfair to truncators. 

Say the 26C we're just here to elect C and don't care about any other 
candidate voters use a 
random-fill strategy, each tossing a fair coin to decide between voting CB or 
CA; then even if as
few as 4 of them vote CA they will elect C. Their chance making C the decisive 
winner is  99.9956% 
(according to an online calculator http://stattrek.com/Tables/Binomial.aspx  ).

I have some sympathy with the idea of giving up something so as to counter 
order-reversing buriers,
but not with the idea that electing a CW is obviously so wonderful that when 
there is no voted CW
we must guess that there is a sincere CW and if we can infer that that can 
only (assuming no voters
are order-reversing) be X then we must elect X.


Chris Benham


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[EM] Beatpath GMC compliance a mistaken standard? (was GMC compliance...)

[Chris Benham]

Marcus,
 
You wrote (29 Dec,2008):
 
You wrote: All three candidates have a majority beatpath
to each other, so GMC says that any of them are allowed to
win. No! Beatpath GMC doesn't say that any of them are
allowed to win; beatpath GMC only doesn't exclude any of
them from winning. 


I can't see that the distinction between allowed to win and 
not excluded from winning is anything more than that between
the glass is half full and the glass is half empty, so I reject your
semantic quibble. Any candidate that a criterion C doesn't exclude
from winning is (as far as C is concerned) allowed to win.
 
You didn't demonstrate that the GMC concept is spectacularly
vulnerable to mono-add-plump. 
 
Well, I think I did. Perhaps you misunderstand my use of the 
word concept.

Beatpath GMC says that the winner must come from a certain set
S, but a candidate X can fall out of  S if a relatively large number
of new ballots are added, all plumping (bullet-voting) for X.
 
Is there any other criterion with that absurd feature?

However, the fact, that Schulze(winning votes) satisfies
mono-add-plump and always chooses from the CDTT set and
isn't vulnerable to irrelevant ballots, shows that these
properties are not incompatible.

Yes, and I never meant to suggest otherwise.  In your previous post
you (referring to beatpath GMC as the CDTT criterion) wrote:
 
When Woodall's CDTT criterion is violated, then this
means that casting partial individual rankings could
needlessly lead to the election of a candidate B who
is not a Schwartz candidate; needlessly because
Woodall's CDTT criterion is compatible with the
Smith criterion, independence of clones, monotonicity,
reversal symmetry, Pareto, resolvability, etc..

The Schwartz criterion doesn't imply beatpath GMC, so
by a Schwartz candidate you mean a '[presumed] sincere 
Schwartz candidate' instead of a  'voted Schwartz candidate'.
 
I don't accept that this stated aim is necessarily so desirable
partly because it isn't the case that (assuming sincere voting
and no strategic nominations) a Schwartz candidate is the
one that is mostly likely to be the SU winner (as evidenced by
my suggested Comprehensive 3-slot Ratings Winner criterion's
incompatibility with Condorcet).

Secondly I don't accept your suggestion that compliance with
beatpath GMC is acceptably cheap (let alone free) because it
isn't compatible with recently suggested Smith- Comprehensive 3-slot
Ratings Winner criterion, which I value much more.

In other words the CDTT set can fail to include the candidate that on
overwhelming common-sense (mostly positional) grounds is the strongest
candidate (e.g. C in Situation # 2).
 
So given a method that meets what I've been recently calling Strong
Minimal Defense  (and so Minimal Defense and Plurality) and Schwartz
(and so fails LNHarm and meets Majority for Solid Coalitions), I consider
the addition of compliance with beatpath GMC a negative if without it the
method can meet Smith- Comprehensive 3-slot Ratings Winner (which
should be very very easy).


Chris Benham


 

Dear Chris Benham,

you wrote (29 Dec 2008):

The  Generalised Majority Criterion says in effect that
the winner must come from Woodall's CDTT set, and is
defined by Markus Schulze thus (October 1997):

 Definition (Generalized Majority Criterion):

 X  Y means, that a majority of the voters prefers    X to Y.

    There is a majority beat-path from X to Y, means,
    that X  Y or there is a set of candidates
    C[1], ..., C[n] with X  C[1]  ...  C[n]  Y.

    A method meets the Generalized Majority
    Criterion (GMC) if and only if:
    If there is a majority beat-path from A to B, but
    no majority beat-path from B to A, then B must not
    be elected.

With full strict ranking this implies Smith, and obviously 
Candidates permitted to win by GMC (i.e.CDTT), Random
Candidate is much better than plain Random Candidate.
Nonetheless I think that compliance with GMC is a mistaken
standard in the sense that the best methods should fail it.

The GMC concept is spectacularly vulnerable to Mono-add-Plump!

[Situation #1]

25: AB
26: BC
23: CA
04: C
78 ballots (majority threshold = 40)

BC 51-27,   CA 53-25,   AB 48-26.

All three candidates have a majority beat-path to each other,
so GMC says that any of them are allowed to win.

[Situation #2]

But say we add 22 ballots that plump for C:

25: AB
26: BC
23: CA
26: C
100 ballots (majority threshold = 51)

BC 51-49,   CA 75-25,   AB 48-26.

Now B has majority beatpaths to each of the other candidates
but neither of them have one back to B, so the GMC says that
now the winner must be B.

The GMC concept is also naturally vulnerable to Irrelevant
Ballots. Suppose we now add 3 new ballots that plump for an
extra candidate X.

[Situation #3]

25: AB
26: BC
23: CA
26: C
03: X
103 ballots (majority threshold = 52)

Now B no longer has a majority-strength beat-path to C,
so now GMC says that C (along with B) is allowed to win
again.

(BTW this whole demonstration

[EM] Beatpath GMC compliance a mistaken standard? (was GMC compliance...)

[Chris Benham]

Marcus,

You wrote (8 Jan 2009):

Statement #1: Criterion X does not imply criterion Y.
Statement #2: Criterion X and criterion Y are incompatible.

Statement #1 does not imply statement #2. But in your
29 Dec 2008 mail, you mistakenly assume that statement #1
implies statement #2.

No I didn't. That is just your mistaken impression.

You proved only that beatpath GMC does not imply mono-add-plump;
but then you mistakenly concluded that this means that beatpath
GMC and mono-add-plump were incompatible (spectacularly
vulnerable to mono-add-plump, spectacular failure of
mono-add-plump).

No,  I only wrote that the beatpath GMC *concept* is vulnerable to 
Mono-add-Plump.  

However, the fact, that Schulze(winning votes) satisfies beatpath GMC 
and mono-add-plump, demonstrates that these two criteria are not incompatible.

Yes, that is obvious. I explicitly acknowledged this in my last post.

I think that all methods that fail Independence from Irrelevant Ballots are 
silly and
that methods should meet the Majority criterion.  The Majority *concept* is 
vulnerable to Irrelevant Ballots because candidate A can be the only candidate
allowed to win by the Majority criterion and then we add a handful of ballots 
that
all plump for nobody and candidate A no longer has a majority.

But of course I don't suggest that those two criteria are incompatible.

The point of my  Dec.29 demonstration was to refute any notion or assumption
that all candidates in the CDTT (i.e. those not excluded by Beatpath GMC) must
be stronger (i.e. more representative of the voters and so more deserving of 
victory)
than any of the candidates outside the CDTT. 

This was only the first part of my argument that  Beatpath GMC [compliance] is a
mistaken standard. What other criterion/standard says that the winner must 
come
from set S, with S being a set that a candidate X can be kicked out of by an 
influx
of new ballots that all plump (bullet-vote) for X?

I put it to you that the answer is none, and that that makes Beatpath GMC 
uniquely
weird and suspect. By itself that isn't conclusively damning because it doesn't 
prove
that Beatpath GMC can exclude the strongest candidate. 

25: AB
26: BC
23: CA
26: C

But I contend that here in my situation 2 election Beatpath GMC does exclude
the clearly strongest candidate C.  You ignored the last few paragraphs of my 
last post:

.. I don't accept your suggestion that compliance with beatpath GMC is 
acceptably cheap 
(let alone free), because it isn't compatible with my recently suggested 
Smith- Comprehensive 
3-slot Ratings Winner criterion, which I value much more.

http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023595.html

In other words the CDTT set can fail to include the candidate that on 
overwhelming 
common-sense (mostly positional) grounds is the strongest candidate (e.g. C in 
Situation # 2).
 
So given a method that meets what I've been recently calling Strong Minimal 
Defense  
(and so Minimal Defense and Plurality) and Schwartz (and so fails LNHarm and 
meets Majority 
for Solid Coalitions), I consider the addition of compliance with beatpath 
GMC a negative if 
without it the method can meet Smith- Comprehensive 3-slot Ratings Winner 
(which
should be very very easy).

Chris Benham




Dear Chris Benham,

you wrote (29 Dec 2008):

 I think that compliance with GMC is a mistaken standard
 in the sense that the best methods should fail it.

 The GMC concept is spectacularly vulnerable to Mono-add-Plump!

 [Situation #1]

 25: AB
 26: BC
 23: CA
 04: C
 78 ballots (majority threshold = 40)

 BC 51-27,  CA 53-25,  AB 48-26.

 All three candidates have a majority beat-path to each other,
 so GMC says that any of them are allowed to win.

 [Situation #2]

 But say we add 22 ballots that plump for C:

 25: AB
 26: BC
 23: CA
 26: C
 100 ballots (majority threshold = 51)

 BC 51-49,  CA 75-25,  AB 48-26.

 Now B has majority beatpaths to each of the other candidates
 but neither of them have one back to B, so the GMC says that
 now the winner must be B.

 The GMC concept is also naturally vulnerable to Irrelevant
 Ballots. Suppose we now add 3 new ballots that plump for an
 extra candidate X.

 [Situation #3]

 25: AB
 26: BC
 23: CA
 26: C
 03: X
 103 ballots (majority threshold = 52)

 Now B no longer has a majority-strength beat-path to C,
 so now GMC says that C (along with B) is allowed to win
 again.

 (BTW this whole demonstration also applies to Majority-Defeat
 Disqualification(MDD) and if we pretend that the C-plumping
 voters are truncating their sincere preference for B over A
 then it also applies to Eppley's Truncation Resistance
 and Ossipoff's SFC and GFSC criteria.)

I wrote (29 Dec 2008):

 Your argumentation is incorrect. Example:

    In many scientific papers, the Smith set is criticized
    because the Smith set can contain Pareto-dominated
    candidates. However, to these criticisms I usually
    reply that the fact

[EM] Beatpath GMC compliance a mistaken standard?

[Chris Benham]

Kevin,

You wrote (10 Jan 2009):

26 AB
25 BA
49 C

Mutual Majority elects {A,B}

Now add 5 A bullet votes:

26 AB
25 BA
49 C
5 A

Now Mutual Majority elects {A,B,C}.

Oops!  (I knew that!)  Sorry for falsely contradicting you.

Why is mono-add-plump important?

Because as an election method algorithm that fails it
simply can't have any credibility as a quasi-intelligent 
 device (which is what it is supposed to be) and because 
 satisfying it should be (and is) very cheap.

I feel that cheapness isn't relevant to whether a criterion is important,
and certainly not to whether failing it is absurd. I save the term 
absurd for ideas that are bad regardless of what else is available.

Well I don't. If none of the election criteria were incompatible with each
other, wouldn't we say that nearly all of them are important?

Regarding your first reason: Why is it acceptable to fail mono-add-top
or Participation, but not acceptable to fail mono-add-plump? I guess
that you based this distinction almost entirely on the relative cheapness
of the criteria.

No. With mono-add-top and Participation, the quasi-intelligent device in
reviewing its decision to elect X gets (possibly relevant) information about
other candidates besides X. With mono-add-plump it gets nothing but information
about and purely in favour of X, so it has no excuse at all for changing its 
mind
about electing X.

 If we view CDTT somehow as an election method, then when it fails 
 mono-add-plump, the bullet votes for X are not simply strengthening
X, they are also *weakening* some pairwise victory of Y over Z, which X
had relied upon in order to have a majority beatpath to Z.

That just testifies to the absurdity of an algorithm  specifically putting 
some  
 special significance on majority beatpaths versus other beatpaths.

You're saying it's absurd, but what is absurd about it?

It's absurd that ballots that plump for X should in any way be considered 
relevant
to the strength of the pairwise comparison between two other candidates.
This absurdity only arises from the algorithm specifically using (and relying 
on) a
majority threshold.   

It would be better, as in less arbitrary, if you simply criticized that 
beatpath GMC is 
incompatible with ratings summation.

So is Condorcet. I don't think it's particularly arbitrary  to value electing 
a voted
Shwartz winner. I'm still a bit confused as to why anyone would be interested in
beatpath GMC.

So essentially, Schwartz//Approval is preferable to any method that satisfies 
SMD, 
Schwartz, and beatpath GMC.

Yes, much preferable to any method that satisfies beatpath GMC period

I don't feel there's an advantage to tending to elect candidates with more 
approval, because 
in turn this should just make voters approve fewer candidates when they doubt 
how the method 
will use their vote.

And why is that a negative?  I value LNHarm as an absolute guarantee, but in 
inherently- 
vulnerable-to-Burial  Condocet methods, I think it is better if they have a 
watch who you rank
because you could help elect them Approval flavour.

From your earlier post:
In the three-candidate case, at least, I think it's a problem to elect a 
candidate who isn't in the 
CDTT.

Why?

25: AB
26: BC
23: CA
26: C

In this situation 2 election from my demonstration, can you seriously contend 
(with a straight face)
that electing C is a problem?   Refresh my memory: who first suggested  Max. 
Approval Opposition 
as a way of measuring a candidate's strength?


Chris Benham


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[EM] Beatpath GMC compliance a mistaken standard?

[Chris Benham]

Kevin,

You wrote (11 Jan 2009):

There are reasons for criteria to be important other than how easy they are 
to satisfy. 
Otherwise why would we ever bother to satisfy the difficult criteria?

Well, if  as I said none of the criteria were incompatible with each other 
then
presumably none of the criteria would be difficult.

With mono-add-top and Participation, the quasi-intelligent device in
reviewing its decision to elect X gets (possibly relevant) information 
about other candidates besides X.

How can it be relevant? X was winning and X is the preferred candidate
on the new ballots.

You know that Condorcet is incompatible with mono-add-top (and so of course
Participation), so if we value compliance with the Condorcet criterion 
information
about candidates ranked below X must sometimes be relevant. But even if  the 
quasi-intelligent device is mistaken in treating them as relevant, then that is 
a much
more understandable  and much less serious a blunder than the mono-add-plump
failure.

It's absurd that ballots that plump for X should in any way be considered 
 relevant to the strength of the pairwise comparison between two other 
 candidates.
This absurdity only arises from the algorithm specifically using (and relying 
on) 
 a majority threshold.
 
We have Mutual Majority and beatpath GMC displaying the same phenomenon.
 
No. I don't accept that 'being tossed out of the favoured (not excluded from 
winning)
set' is exactly the same phenomenon as 'being joined by others in the 
favoured set'.
The latter is obviously far less serious.

I don't feel there's an advantage to tending
to elect candidates with more approval, because 
in turn this should just make voters approve fewer
candidates when they doubt how the method 
will use their vote.

And why is that a negative?  I value LNHarm as an absolute
guarantee, but in inherently- vulnerable-to-Burial  Condocet 
 methods, I think it is better if they have a watch who you rank
because you could help elect them Approval flavour.

This is a negative because it suggests that your positional criterion
will be self-defeating.
 
How can it possibly be self-defeating?  What is there to defeat?

From your earlier post:
In the three-candidate case, at least, I think it's a problem to elect a 
 candidate who isn't in the CDTT.

Why?

Because in the three-candidate case this is likely to be a failure of MD or 
SFC, 
or close to it.
 
I'm happy to have MD, and I don't care about SFC or close failures of  MD.
 
 I'm still a bit confused as to why anyone would be interested in
beatpath GMC.

Well, it's a majority-rule criterion that is compatible with clone
independence and monotonicity.
 
Other majority-rule criteria with those same properties will suffice. 

In the three-candidate case it's also compatible with LNHarm. By adding a vote 
for 
your second choice, you can't inadvertently remove your first preference from 
the CDTT.
 
Well since Condorcet is incompatible with LNHarm, that doesn't explain why 
Condorcet
fans should like it.  Also I think this is mainly just putting a positive spin 
on gross unfairness
to truncators and the related silly random-fill incentive.
 
25: AB
26: BC
23: CA
26: C
100 ballots (majority threshold = 51)

BC 51-27,   CA 75-25,   AB 48-26.
 
In Schulze(Winning Votes), and I think also in any method that meets beatpath 
GMC
and mono-raise, the 26C truncators can virtually guarantee that C be elected by 
using
the random-fill strategy. That is silly and unfair.
 
Also, by artificially denying  the clearly strongest candidate  any method that 
doesn't
elect C must be vulnerable to Pushover, certainly much more than those that do 
elect C.

http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023590.html
 
(not that that is a very relevant strategy problem for the methods like WV that 
have the
much easier and safer random-fill strategy for the C(B=C) voters.)
 

Chris  Benham


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[EM] Schulze (Approval-Domination prioritised Margins)

[Chris Benham]

I have an idea for a new defeat-strength measure for the Schulze algorithm
(and  similar such as Ranked Pairs and River), which I'll call:

Approval-Domination prioritised Margins:

*Voters rank from the top however many candidates they wish.
Interpreting ranking (in any position, or alternatively above at least one other
candidate) as approval, candidate A is considered as approval dominating
candidate B if  A's approval-opposition to B (i.e. A's approval score on ballots
that don't approve B) is greater than B's total approval score.

All pairwise defeats/victories where the victor approval dominates the loser
are considered as stronger than all the others.

With that sole modification, we use Margins  as the measure of  defeat 
strength.*

This aims to meet  SMD  (and so Plurality and Minimal Defense, criteria failed
by regular Margins) and my recently suggested Smith- Comprehensive 3-slot
Ratings Winner criterion (failed by Winning Votes).

http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023595.html

Here is an example where the result differs from regular Margins, Winning Votes
and  Schwartz//Approval.

44: A
46: BC
07: CA
03: C

AB  51-46 =  5 * 
BC  46-10 = 36 
CA  56-44 = 12

Plain Margins would consider B's defeat to be the weakest and elect B, but that 
is the only
one of the three pairwise results where the victor approval-dominates the 
loser.  A's approval
opposition to B is 51, higher than B's total approval score of 46.

So instead my suggested alternative considers A's defeat (with the next 
smallest margin) to be
the weakest  and elects A.  Looking at it from the point of view of the Ranked 
Pairs algorithm
(MinMax, Schulze, Ranked Pairs, River are all equivalent with three 
candidates), the AB result
is considered strongest  and so locked, followed by the BC result (with the 
greatest margin)
to give the final order ABC.

Winning Votes  considers C's defeat to be weakest and so elects C.  
Schwartz//Approval also
elects C.

Margins election of  B is a failure of  Minimal Defense. Maybe the B supporters 
are Burying
against A and A is the sincere Condorcet winner.

I have a second suggestion for measuring defeat strengths which I think is 
equivalent to
Schwartz//Approval, and that is simply Loser's Approval (interpreting ranking 
as approval as
above, defeats where the loser's total approval score is higher are considered 
to be weaker than
those where the loser's total approval score is lower).

Some may see this as more elegant than Schwartz//Approval, and maybe in some 
more complicated
example it can give a different result.


Chris Benham


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Re: [EM] Beatpath GMC compliance a mistaken standard?

[Chris Benham]

Kevin,

I can't see what's so highly absurd about failing mono-append. It's
basically a limited case of mono-raise, and one that doesn't seem
especially more important. Is it absurd to fail mono-raise?

The absurdity of failing mono-append is compounded by the cheapness of
meeting it. As with mono-add-plump the quasi-intelligent device is given
simple and pure new information. Being confused by it is simply unforgivable
*stupidity* on the part of  the quasi-intelligent device.

Regards mono-raise, I would say that failing it is obviously 'positionally 
absurd'
and 'pairwise absurd' but perhaps not  'LNH absurd'.  We know that it isn't 
absurd in the sense that mono-add-plump and mono-append is, because it is 
failed by a method that has a maximal set of  (IMO) desirable criterion 
compliances .

 Can I take it then that you no longer like 
 CDTT,Random Ballot, which does award
 a probability pie?

Sure. Does your question mean that this really is how you view the
difference between CDTT and Mutual Majority, is in terms of the candidates
of the winning set sharing a probability pie?

Not exactly. No-one has ever suggested  MM,Random Ballot as a good method and 
few
have suggested  that sometimes the clearly most appropriate winner is not in 
the MM set
(as I have regarding the CDTT set).

 The criterion/standard is an end in itself.  Not
 everything is about the strategy game.
 Higer SU with sincere voting and sparing the method
 common-sense  (at least) difficult -to-counter complaints 
 from the positional-minded are worthwhile accomplisments.

This strikes me as an unusual amount of paranoia that the method's
results can't be explained to the public's satisfaction unless it's
similar to Approval.

It isn't just the public. It is myself wearing my common-sense positional 
hat. And it isn't just
Approval, it's  'Approval and/or FPP'.


Chris Benham








Hi Chris,

--- En date de : Jeu 15.1.09, Chris Benham cbenha...@yahoo.com.au a écrit :
 Kevin,
 
 You wrote (12 Jan 2009):
 
 Why do we *currently* ever bother to satisfy
 difficult criteria? What do 
 we mean when we say we value a criterion? Surely not just
 that we feel 
 it's cheap?
 
 When simultaneously a criterion's satisfaction's
 cost falls below a certain 
 level and  its failure reaches a certain level of 
 absurdity/silliness  I start to
 lose sight of  the distinction between important for
 its own sake and very
 silly not to have because it's so cheap.
 Mono-add-plump (like mono-append)
 is way inside that territory.  

I see. I don't think I value criteria for this sort of reason. If I insist
on a criterion like Plurality, it's because I don't think the public
will accept the alternative. And these two criteria are relative, so
that in order to complain about a violation you have to illustrate a
hypothetical scenario in addition to what really occurred.

I can't see what's so highly absurd about failing mono-append. It's
basically a limited case of mono-raise, and one that doesn't seem
especially more important. Is it absurd to fail mono-raise?

 If you need to identify majorities, then the fact
 that a ballot shows
 no preference between Y and Z, is relevant
 information.
 
 In my view a voting method *doesn't* need to
 specifically identify majorities, so it
 isn't. (The voting method can and should meet
 majority-related criteria 'naturally'
 and obliquely.)

But we aren't even talking about voting methods, we're talking about
sets. You have basically criticized Schulze(wv) even though it naturally 
and obliquely satisfies majority-related criteria.

 But even if  the quasi-intelligent device is mistaken
 in treating them as
 relevant, then that is a much more understandable  and
 much less serious a 
 blunder than the mono-add-plump failure.
 
 Ok. I still don't really see why, or what makes
 the difference.
 
 Imagine the quasi-intelligent device is the captain of  a
 democracy bus that takes
 on passengers and then decides on its course/destination
 after polling the passengers.
 
 Imagine that as in situation 1 it
 provisionally decides to go to C, and then as in 
 situation 2 a group of new passengers get on
 (swelling the total by about 28%) and 
 they are openly polled and they all say we want to go
 to C, and have nothing else to say
 and then the captain announces in that case I'll
 take the bus to B.
 
 Would you have confidence that that captain made rational
 decisions on the most
 democratic (best representing the
 passengers' expressed wishes) decisions?
 I and I think many others would not, and would conclude
 that  the final B decision
 can only be right if the original C decision
 was completely ridiculous. Or would you
 be impressed by the captain's wisdom in being properly
 swayed by the new passengers'
 indecision between A and B?

However I answer doesn't make any difference, because the question is
why this crosses the boundary of clear badness while failures of 
mono-add-top

[EM] Beatpath GMC compliance a mistaken standard?

[Chris Benham]

Kevin,

You wrote (25 Jan 2009):

I think there ought to be a clear distinction between criteria whose
violation is absurd no matter what the circumstances, and criteria
whose violation is absurd due to other available options.

I don't see why (particularly).

There are very few (named) criteria whose failure I'd call absurd no
matter what.

Of those criteria, which is the one you consider to be the least absurd?
(Or if you can't say, just name some.)

 Does your question mean that this really is how you view the
 difference between CDTT and Mutual Majority, is in terms of
 the candidates of the winning set sharing a probability pie?
 
 Not exactly. No-one has ever suggested  MM,Random Ballot as a 
 good method and few have suggested  that sometimes the clearly most
 appropriate winner is not in the MM set (as I have regarding the CDTT set).

I think that either isn't relevant or doesn't help your case.

Then you can regard that as a rhetorical aside. To answer your question again
I would say that way of putting it seems too mild to me, but I can't see that 
it's
irrational.

The question is about why you view MM's behavior as qualitatively different
from CDTT's behavior, when in practice, in a real method, it's exactly the same 
behavior.

In a previous message I think I made it clear that I don't accept that it is 
exactly
the same behavior.

[I don't accept that 'being tossed out of the favoured (not excluded from 
winning)
set' is exactly the same phenomenon as 'being joined by others in the 
favoured set'.]

Well, supposing that the public decided to accept a method that failed
a positional criterion, I guess at that time I would drop that criterion.

Does that mean that you think all positional criteria have no value other 
than to appease
misguided members  of  the public?

Hypothetically if the public were willing to accept any method I would
propose to them, and not question any of its results, then I wouldn't care
about appearances. I would just give them the method that I felt would
perform the best.

In this context, what  do you mean by appearances?  How can a method that you 
feel 
performs the best have (in your eyes) anything wrong with its appearance?

Chris Benham



Hi Chris,

--- En date de : Ven 23.1.09, Chris Benham cbenha...@yahoo.com.au a écrit :
 I can't see what's so highly absurd about
 failing mono-append. It's
 basically a limited case of mono-raise, and one that
 doesn't seem
 especially more important. Is it absurd to fail
 mono-raise?
 
 The absurdity of failing mono-append is compounded by the
 cheapness of
 meeting it. As with mono-add-plump the quasi-intelligent
 device is given
 simple and pure new information. Being confused by it is
 simply unforgivable
 *stupidity* on the part of  the
 quasi-intelligent device.

I find it unclear how to decide whether something is unforgivably stupid
in your view, or instead mitigated by something like this:

 Regards mono-raise, I would say that failing it is
 obviously 'positionally absurd'
 and 'pairwise absurd' but perhaps not  'LNH
 absurd'.  We know that it isn't 
 absurd in the sense that mono-add-plump and
 mono-append is, because it is 
 failed by a method that has a maximal set of 
 (IMO) desirable criterion compliances .

It seems to me like a real problem that the absurdity of failing a
criterion can depend on whether better criteria require that it be
failed. I think this is just cheapness again. Failing mono-raise
isn't absurd, because mono-raise is relatively expensive.

I think there ought to be a clear distinction between criteria whose
violation is absurd no matter what the circumstances, and criteria
whose violation is absurd due to other available options.

There are very few (named) criteria whose failure I'd call absurd no
matter what.

  Can I take it then that you no longer like 
  CDTT,Random Ballot, which does award
  a probability pie?
 
 Sure. Does your question mean that this really is how
 you view the
 difference between CDTT and Mutual Majority, is in terms of
 the candidates
 of the winning set sharing a probability pie?
 
 Not exactly. No-one has ever suggested  MM,Random
 Ballot as a good method and few
 have suggested  that sometimes the clearly most
 appropriate winner is not in the MM set
 (as I have regarding the CDTT set).

I think that either isn't relevant or doesn't help your case. The
question is about why you view MM's behavior as qualitatively different
from CDTT's behavior, when in practice, in a real method, it's exactly
the same behavior. If the important thing is how many people suggest
that the clearly best winner is not in the MM or CDTT sets, then there
doesn't seem to be a good reason to bring up mono-add-plump.

  The criterion/standard is an end in itself.  Not
  everything is about the strategy game.
  Higer SU with sincere voting and sparing the method
  common-sense  (at least) difficult -to-counter
 complaints 
  from the positional-minded are worthwhile
 accomplisments

[EM] voting strategy with rank-order-with-equality ballots

[Chris Benham]

Warren,

How true is it that approval-style voting is strategic for Schulze?

Not very true. It depends on the voter's information and  sincere ratings.
Schulze, being a Condorcet method fails Favourite Betrayal.

Is Schulze with approval-style ballots a better or worse voting system 
than plain approval?

If approval-style ballots are compelled than Schulze is the same as plain
Approval.  If they are merely allowed  (as Marcus Schulze and other 
proponents favour) then in my opinion it is better than Approval.

In the zero-information case, the voter with a big enough gap in hir sincere 
ratings
does best to rank all the candidates above the gap equal top and to strictly
rank all those below it  (random-filling if necessary in the absence of a 
sincere
full ranking).

I find it preferable that the zero-info. strategy for a ranked-ballot method be 
either
full sincere ranking regardless of  relative ratings (as in IRV and Margins) 
or  sincere
ranking above the big ratings gap and truncation below it  (as in 
Smith//Approval).

By  Shulze  I have been meaning  Shulze(Winning Votes), the 'standard version'
favoured by Marcus himself and other proponents. 

In January this year I suggested a different version I prefer:

http://lists.electorama.com/pipermail/election-methods-electorama.com/2009-January/023959.html


Chris Benham


 
 Warren Smith wrote (8 June 2009):

One problem is nobody really has a good understanding of what good strategy is.

If one believes that range voting becomes approval voting in the
presence of strategic voters (often, anyhow)...

One might similarly speculate that
strategic voters in a system such as Schilze beatpaths ALLOWING ballots
with both  and = (e.g. AB=C=DE=F is a legal ballot)  usually the
strategic vote
is approval style i.e. of form A=B=CD=E=F, say, with just ONE .
One might then speculate that Schulze, just like range, then becomes
equivalent to approval voting for strategic voters.

Well...  how true or false is that?   Is Schulze with approval-style ballots
a better or worse voting system than plain approval?

How true is it that approval-style voting is strategic for Schulze?

I'd like to hear people's ideas on this question.  (And not
necessarily just for Schulze -- substitute other methods too, if you
prefer.)

The trouble is, range voting is simple. Simple enough that you can
reach a pretty full understanding of what strategic range voting is.
  (Which is not at all trivial,
but it can pretty much be done.) In contrast, a lot of Condorcet
systems including Schulze are complicated. Complicated enough that
making confident statements
about their behavior with strtagic voters (or even undertsnading what
strtagy IS) is
hard.

Frankly, I've heard various vague but confident claims about strategy
for Schulze  the like, and my impression is those making the claims
know very little about what they
are talking about.  I also know very little on this, the difference is
I admit it :)


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[EM] voting strategy with rank-order-with-equality ballots

[Chris Benham]

Kevin,

I have found that Schulze(wv) had little favorite betrayal incentive. In 
simulations I mentioned in June 05, out of 50,000 trials, Schulze(wv) showed 
incentive 7 times, compared to 251 for Schulze(margins), 363 for 
Condorcet//Approval, and 625 for my erroneous interpretation of 
ERBucklin(whole).

What was this erroneous interpretation?  How can a method that meets 
Favourite Betrayal, such as ER-Bucklin(whole) ever show favourite
betrayal incentive?

Chris Benham


 

Kevin Venzke wrote (9 June 2009):

Hello,

I think in Schulze(wv) and similar, decent methods, you shouldn't rank the 
worse of two frontrunners or below. I don't think that's a big problem though.

I have found that Schulze(wv) had little favorite betrayal incentive. In 
simulations I mentioned in June 05, out of 50,000 trials, Schulze(wv) showed 
incentive 7 times, compared to 251 for Schulze(margins), 363 for 
Condorcet//Approval, and 625 for my erroneous interpretation of 
ERBucklin(whole).

The simulation worked by examining the effects of introducing a strict ranking 
between two candidate ranked tied at the top. So a method showed favorite 
betrayal incentive when introducing a strict ranking AB moved the win to one 
of these candidates from a third candidate.

You can look at incentive to compress at the top, but it's not as informative. 
There is compression incentive where introducing the AB strict ranking moves 
the win e.g. from B to a third candidate. This happened hundreds of times for 
the methods I looked at (1200 for ICA).

I guess you could look at the odds that a strict ranking will help or hurt 
compared to an equal ranking, overall. I'm not sure that would be very 
informative either though. For one thing, it would only tell you about the 
zero-info case. And it wouldn't consider utility, which should be important: 
Whether or not you should compress at the top probably depends on how much you 
like those candidates compared to the other candidates.

Kevin Venzke


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[EM] Condorcet/Range DSV

[Chris Benham]

Jameson,

This Condorcet-Range hybrid you suggest seems to me to inherit a couple of
the problems with Range Voting. 

It fails the Minimal Defense criterion.

49: A100,  B0,  C0
24: B100,  A0,  C0
27: C100,  B80, A0

More than half the voters vote A not above equal-bottom and below B, and yet
A wins.

Also I don't like the fact that the result can be affected just by varying the 
resolution
of  ratings ballots used, an arbitrary feature.

I think it would be better if the method derived approval from the ballots, 
approving all
candidates the voter rates above the voter's average rating of  the Smith set 
members.


For strategies which don't change the content
of the Smith set, it does very well on other criteria, fulfilling
Participation, Consistency, and Local IIA. 


The criteria you mention only apply (as a strict pass/fail test) to voting 
methods, not 
strategies (and  have nothing to do with strategy).

We know that Condorcet is incompatible with Participation  (and so I suppose 
also with
the similar Consistency).  I don't see how a method that fails Condorcet Loser 
can meet
Local IIA.

And because it uses Range ballots as an input but encourages
more honest voting than Range,..

That is more true of the automated approval version I suggested, and also it 
isn't
completely clear-cut because Range meets Favourite Betrayal which is 
incompatible
with Condorcet.

 
Chris Benham


Jameson Quinn wrote (25 June 2009) wrote:


 
I believe that using Range ballots, renormalized on the Smith set as a
Condorcet tiebreaker, is a very good system by many criteria. I'm of course
nothttp://lists.electorama.com/pipermail/election-methods-electorama.com/2005-January/014469.htmlthe
first one to propose this method, but I'd like to justify and analyze
it further.

I call the system Condorcet/Range DSV because it can be conceived as a kind of
Declared Strategy Voting system, which rationally strategizes voters' ballots 
for them assuming that
they have correct but not-quite-complete information about all other voters.
Let me explain.

I have been looking into fully-rational DSV methods using Range ballots both
as input and as the underlying method in which strategies play out. It turns
out to be impossible, as far as I can tell, to get a stable, deterministic,
rational result from strategy when there is no Condorcet winner. (Assume
there's a stable result, A. Since A is not a cond. winner, there is some B
which beats A by a majority. If all BA voters bullet vote for B then B is a
Condorcet winner, and so wins. Thus there exists an offensive strategy. This
proof is not fully general because it neglects defensive strategies, but in
practice trying to work out a coherent, stable DSV which includes defensive
strategies seems impossible to me.) Note that, on the other hand, there MUST
exist a stable probabilistic result, that is, a Nash equilibrium.

Let's take the case of a 3-candidate Smith set to start with. (This
simplifies things drastically and I've never seen a real-world example of a
larger set.) In the Nash equilibrium, all three candidates have a nonzero
probability of winning (or at least, are within one vote of having such a
probability). Voters are dissuaded from using offensive strategy by the real
probability that it would backfire and result in a worse candidate winning.
This Nash equilibrium is in some sense the best result, in that all voters
have equal power and no voter can strategically alter it. However, it is
both complicated-to-compute and unnecessarily probabilistic. Forest Simmons has
proposed an interesting
methodhttp://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/011028.htmlfor
artificially reducing the win probability of the less-likely
candidates,
but this method increases computational complexity without being able to
reach a single, fully stable result. (Simmons proposed simply selecting the
most-probable candidate, which is probably the best answer, but it does
invalidate the whole strategic motivation).
There's an easier way. Simply assume that any given voter has only
near-perfect information, not perfect information. That is, each voter knows
exactly which candidates are in the Smith set, but makes an ideosyncratic
(random) evaluation of the probability of each of those candidates winning.
That voter's ideal strategic ballot is an approval style ballot in which all
candidates above their expected value are rated at the top and all
candidates below at the bottom. However, averaging over the different
ballots they'd give for different subjective win probabilities, you get
something very much like a range ballot renormalized so that there is at
least one Smith set candidate at top and bottom. (It's not exactly that, the
math is more complex, especially when the Smith set is bigger than 3; but
it's a good enough approximation and much simpler than the exact answer).

Let's look at a few scenarios to see how this plays out

Re: [EM] Condorcet/Range DSV

[Chris Benham]

Jameson,

Sorry to be so tardy in replying.

 
That is not a bad suggestion; I like both systems. Yours gives less of a 
motivation for 
honest rating: In most cases, it makes A100 B99 C0 equivalent to A100 B51 C0.

No, mine gives more motivation for honest rating (in the sense that it gives 
less incentive 
for dishonest rating).   If  A, B, C  are the three Smith-set members then 
it makes both
A100, B99, C0 and  A100, B51, C0  equivalent to A100, B100, C0.

I guess you'd give exactly half an approval if B were at exactly 50?

Yes.

49: A100,  B0,  C0
24: B100,  A0,  C0
27: C100,  B80, A0

More than half the voters vote A not above equal-bottom and below B, and yet
A wins.

True. Yet B could win if the C voters rated B 99, which would still be 
Condorcet-honest.

That isn't really in principle relevant because your suggested method doesn't 
guarantee to a
section of the voters comprising more than half  who rate/rank A bottom that 
they can ensure
that A loses while still expressing all their sincere pairwise preferences.

4999: A100,  B0,  C0
2500: B100,  A0,  C0
2501: C100,  B99, A0

BA 5001- 4999,  AC,  CB. 

In this modified version of my demonstration that your suggested method fails 
Minimal Defense,
the majority that prefer B to A cannot ensure that B loses and still be 
Condorcet-honest.

Anyway, the main motivations for a DSV-type proposal like this is to make it 
really rare for voters 
to have enough information to strategize without it backfiring. I think that 
including full range information 
(that is, my proposal as opposed to yours) makes the voter's analysis harder, 
and so makes the system  
more resistant to strategy. 

I don't think the type of examples I've given would be really rare, and in 
them I don't think the C
supporters have to very well-informed or clever to work out that their 
candidate can't beat A and
so they have incentive to falsely vote B (at least) equal to their favourite.

Favorite Betrayal in this case means, honest ABC voters who know that A's 
losing and that CBA 
and ACB votes are both relatively common, can vote BAC to cause a Condorcet 
tie and perhaps 
get B to win ...

Not necessarily, no. You seem to be assuming that Favourite Betrayal strategy 
is only about falsely creating
a  Condorcet tie when one's favourite isn't the (presumed to be) sincere 
Condorcet winner. It can
also be the case that the strategist fears that if she votes sincerely there 
will be no Condorcet winner,
so she order-reverse compromises to try to make her compromise the voted 
Condorcet winner.


Chris  Benham







Jameson Quinn wrote  (26 June 2009) :


This Condorcet-Range hybrid you suggest seems to me to inherit a couple of
the problems with Range Voting.

Fair enough.



It fails the Minimal Defense criterion.

49: A100,  B0,  C0
24: B100,  A0,  C0
27: C100,  B80, A0

More than half the voters vote A not above equal-bottom and below B, and yet
A wins.

True. Yet B could win if the C voters rated B 99, which would still be 
Condorcet-honest.



Also I don't like the fact that the result can be affected just by varying the 
resolution
of  ratings ballots used, an arbitrary feature.

I think it would be better if the method derived approval from the ballots, 
approving all
candidates the voter rates above the voter's average rating of  the Smith set 
members.

That is not a bad suggestion; I like both systems. Yours gives less of a 
motivation for honest rating: In most cases, it makes A100 B99 C0 equivalent to 
A100 B51 C0. I guess you'd give exactly half an approval if B were at exactly 
50?

Anyway, the main motivations for a DSV-type proposal like this is to make it 
really rare for voters to have enough information to strategize without it 
backfiring. I think that including full range information (that is, my proposal 
as opposed to yours) makes the voter's analysis harder, and so makes the system 
 more resistant to strategy. Under honest range votes, it also helps improve 
the utility.




For strategies which don't change the content
of the Smith set, it does very well on other criteria, fulfilling
Participation, Consistency, and Local IIA. 

Sorry, I wasn't clear. If the content of the smith set DOES change, this method 
fails all those criteria. See below for argument of why that's not too bad.



And because it uses Range ballots as an input but encourages
more honest voting than Range,..

That is more true of the automated approval version I suggested, and also it 
isn't
completely clear-cut because Range meets Favourite Betrayal which is 
incompatible
with Condorcet.

Favorite Betrayal in this case means, honest ABC voters who know that A's 
losing and that CBA and ACB votes are both relatively common, can vote 
BAC to cause a Condorcet tie and perhaps get B to win (if A would win that tie, 
then A would be winning already, so they can't get their favorite through 
betrayal. In other words, at least it's monotonic

[EM] Electowiki relicensed to Creative Commons Share Alike 3.0

[Chris Benham]

In the Electowiki article on the River method, none of  these 
links work properly:

* First proposal 
* 
* slight refinement 
* 
* More concise definition. In this last version, River is defined 
very similarly to ranked pairs. 
* 
* Example using 2004 baseball scores. This shows how a 
* 14-candidate election winner can be determined much more 
* quickly using River than with RP or Schulze. 

* Early criticism of the River method. This shows that the River 
* method violates mono-add-top and mono-remove-bottom 
 
One is broken and the rest go to the wrong EM post.
 
http://wiki.electorama.com/wiki/River

 
Also, some of my EM posts in the Electorama archive have links 
to other EM posts which also go to the wrong one.
 
 
Chris Benham


  

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[EM] 'Shulze (Votes For)' definition?

[Chris Benham]

Marcus,

I have some questions about your draft (dated  23 June 2009)  Shulze method
paper, posted:

http://m-schulze.webhop.net/schulze1.pdf

On page 13 you define some of the ways of measuring defeat strengths,
two of which are  Votes For and  Votes Against:

snip

Example 5 (
then the strength is measured primarily by the absolute number N[e,f] of votes 
for candidate e.
(N[e,f],N[f,e]) for (N[g,h],N[h,g]) if and only if at least one of the 
following conditions is satisfied: 
1. N[e,f]  N[g,h]. 2. N[e,f] = N[g,h] and N[f,e]  N[h,g]. 
 
Example 6 (votes against): When the strength of the pairwise defeat ef is 
measured by votes against, 
then the strength is measured primarily by the absolute number N[f,e] of votes 
for candidate f. 
(N[e,f],N[f,e]) against (N[g,h],N[h,g]) if and only if at least one of the 
following conditions is satisfied: 
1. N[f,e]  N[h,g]. 2. N[f,e] = N[h,g] and N[e,f]  N[g,h].
 
snip
 
I am a little bit confused as to the exact meaning of the phrase the absolute 
number ..of 
votes for candidate E.
 
Does the number of votes for E mean 'the number of ballots on which E is 
ranked above
at least one other candidate'?
 
Or does it mean something that can be read purely from the pairwise matrix?

Does it mean 'the sum of all the entries in the pairwise matrix that represent 
pairwise votes for E'?

Do the two methods 'Schulze(Votes For)' and  'Shulze(Votes Against)'  meet  
Independence
of  Clones?

I look forward to hearing your clarification.


Chris  Benham
 votes for): When the strength of the pairwise defeat ef is measured by votes 
for, 


  
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[EM] 'Shulze (Votes For)' definition?

[Chris Benham]

Kevin,

Or does it mean something that can be
read purely from the pairwise matrix?

It's the latter, read from the matrix. Absolute number is in contrast to
using margin or ratio.

Thanks for that, but it isn't the concept of absolute number that I'm having
trouble with.

What I don't understand is the difference between winning votes (which I'm
familiar with) and votes for,  as they are both defined on page 13 of Marcus
Shulze's paper, pasted below.


http://m-schulze.webhop.net/schulze1.pdf

snip

Example 3 (
by winning votes, then the strength is measured primarily by the absolute 
number 
N[e,f] of votes for the winner of this pairwise defeat. 

 
snip
 Example 5 (
votes for candidate e. votes for): When the strength of the pairwise defeat ef 
is measured by 
votes for, then the strength is measured primarily by the absolute number 
N[e,f] of winning votes): When the strength of the pairwise defeat ef is 
measured 
 
snip
Chris Benham


  
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[EM] Anyone got a good analysis on limitations of approval and range voting?

[Chris Benham]

Robert Bristow-Johnson wrote (9 Nov 2009):

Of course IRV, Condorcet, and Borda use different methods to tabulate  
the votes and select the winner and my opinion is that IRV (asset  
voting, i might call it commodity voting: your vote is a  
commodity that you transfer according to your preferences) is a  
kabuki dance of transferred votes.  and there is an *arbitrary*  
evaluation in the elimination of candidates in the IRV rounds: 2nd- 
choice votes don't count for shit in deciding who to eliminate (who  
decided that?  2nd-choice votes are as good as last-choice?  under  
what meaningful and consistent philosophy was that decided?), then  
when your candidate is eliminated your 2nd-choice vote counts as much  
as your 1st-choice.

Regarding IRV's philosophy: each voter has single vote that is transferable
according to a rule that meets Later-no-Harm, Later-no-Help and Majority
for Solid Coalitions.

I rate IRV (Alternative Vote with unlimited strict ranking from the top) as the
best of the single-winner methods that meet Later-no-Harm.

Chris Benham


  
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[EM] IRV is best method meeting 'later no harm'?

[Chris Benham]

Steve Eppley wrote (26 Nov 2009):
Can it be said that Later No Harm (LNH) is satisfied by the variation of
IRV that allows candidates to withdraw from contention after the votes are
cast?

No. Take this classic (on EM) scenario:

49: A
24: B
27: CB

A is the normal IRV winner, but in the variation you describe C presumably
withdraws causing B to win.

49: A
24: BC
27: CB

If the B supporters instead of truncating vote BC then C wins. Assuming
C accepts the win the B voters have caused B to lose by not truncating, a 
clear failure of Later-no-Harm.

Steve wrote:
Since IRV is said to satisfy LNH, then one must say Plurality Rule
satisfies LNH too, because Plurality Rule can be viewed as just a
variation of IRV with a smaller limit (one candidate per voter).

Yes, and I did. I listed FPP (First-Preference Plurality or more traditionally
First Past the Post) as a method that meets Later-no-Harm.

I understand that in the US the Alternative Vote is called IRV, but that 
sometimes
various inferior approximations are given the same label.

Chris Benham


  
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[EM] IRV vs Plurality

[Chris Benham]

Kathy Dopp wrote (11 Jan 2010):

snip

Plurality is far better than IRV for many many reasons including:

1. preserves the right to cast a vote that always positively affects
the chances of winning of the candidate one votes for

2. allows all voters the right to participate in the final counting
round in the case of top two runoff or primary/general elections

snip

IRV satisfies both of these. 

Regarding the first,assuming that the candidate one votes for refers 
to the candidate the voter top-ranks, then top-ranking X in an IRV election 
has the same positive effect on X's chance of winning as does voting for
X in a Plurality election.

It is true that sometimes in an IRV election a subset of X's sincere 
supporters may be able to do better for X by top-ranking some non-X,
whereas in Plurality the best strategy for all of X's supporters is always 
just to vote for X; but that is different.

IRV meets Mono-add-top, which means that a voter who top-ranks X
would never have done better for X by staying home.

Having arrived at the voting booth, the X supporter's overwhelmingly 
best probabilistic IRV strategy is to top-rank X.

Regarding Kathy's second point, IRV voters should be allowed to
strictly rank from the top as many candidates as they wish. 
The voter is then free to ensure that s/he participates in the final
counting round by simply ranking all the candidates (or alternatively
if the likely front-runners are known then just make it very likely by
ranking among them).


Chris Benham


  
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[EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws

[Chris Benham]

 than satisfying  Majority Favorite?

Why does Kathy elsewhere defend Top Two Runoff which isn't monotonic?


Chris Benham


  
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[EM] IRV vs Plurality

[Chris Benham]

Dave Ketchum wrote (9 Jan 2010):

 
For a quick look at IRV: 35A, 33BC, 32C

A wins for being liked a bit better than B - 3533.

That C is liked better than A is too trivial for IRV to notice - 6535.

Let one BC voter change to C and C would win over A - 6535.

Let a couple BC voters switch to A and C would win over A - 6337.

Point is that IRV counting often ignores parts of votes.

Dave Ketchum


Yes. 

The implicit assumption seems to be that ignoring parts of votes is 
always a pure negative but not doing so can cause failure of Later-no-Harm
and Later-no-Help, and vulnerability to Burial.

All Condorcet methods fail those criteria, while IRV meets them.

Note that I wrote that IRV is my favourite of the methods that are
invulnerable to Burial strategy and meet Later-no-Harm.

I didn't write that it was necessarily preferable to to all of the methods
that meet the Condorcet criterion.

 
Chris Benham


  
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[EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws

[Chris Benham]

Abd ul-Rahman Lomax wrote  (14 Jan 2010):

snip
Why does Kathy elsewhere defend Top Two Runoff which isn't monotonic?

This opinion, stated as fact, is false. Top Two Runoff is a two-step 
system, and monotonicity doesn't refer to such. It refers to the 
effect of a vote on a single ballot as to the result of that ballot 
only. A vote for a candidate on a primary ballot in TTR will always 
help the candidate supported to make it either to a majority and a 
win, or to make it into the runoff. It never hurts that candidate. 
snip

A vote for any candidate X in any given IRV  counting round will likewise 
help X to a majority win or to make it into the next round.

The contention that a two-step system (meaning requiring voters to make
two trips to the polls) to elect a single candidate isn't allowed to be judged
in aggregate is absurd.

snip
Did supporters of the Lizard vote for the Wizard in order to create the Lizard 
vs. Wizard election in Louisiana? I rather doubt it. But this wouldn't create a 
monotonicity violation, and the problem is created by eliminations, 
it doesn't exist with repeated balloting.
snip

With repeated balloting there are no eliminations?  As I undersatnd it, in
Top Two Runoff all but the top two first-round vote getters are eliminated
if no candidate gets more than half the votes in the first round.

Chris Benham


  
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[EM] IRV vs Plurality ( Kristofer Munsterhjelm )

[Chris Benham]

Kristofer Munsterhjelm wrote (17 Jan 2010):

To me, it seems that the method becomes Approval-like when (number of 
graduations) is less than (number of candidates). When that is the case, 
you *have* to rate some candidates equal, unless you opt not to rate 
them at all.

That won't make much of a difference when the number of candidates is 
huge (100 or so), but then, rating 100 candidates would be a pain. I'd 
say it would be better to just have plain yes/no Approval for a first 
round, then pick the 5-10 most approved for a second round (using 
Range, Condorcet, whatever). Or use minmax approval or PAV or somesuch, 
as long as it homes in on the likely winners of a full vote.

Simply using plain Approval to reduce the field to the top x point scorers
who then compete in the final round seems unsatifactory to me because
of the  Rich Party incentive (clone problem) for parties to field x 
candidates;
and because of the tempting Push-over (turkey raising) strategy incentive.

Chris Benham


  
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[EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws

[Chris Benham]

Abd Lomax wrote (17 Jan 2010):

snip

Chris is Australian, and is one of a rare breed: someone who actually 
understands STV and supports it for single-winner because of LNH 
satisfaction. Of course, LNH is a criterion disliked by many voting 
system experts, and it's based on a political concept which is, quite 
as you say, contrary to sensible negotiation process.
 snip

I endorse IRV (Alternative Vote, with voters able to strictly rank from the top 
however 
many candidates they choose) as a good method, much better than Plurality or 
TTR,
and the best of the methods that are invulnerable to Burial and meet 
Later-no-Harm.

Some of us see elections as primarily a contest and not a negotiation process.

I endorse IRV because it has a maximal set of  (what I consider to be) 
desirable
criterion compliances:

Majority for Solid Coalitions (aka Mutual Majority)
Woodall's Plurality criterion
Mutual Dominant Third
Condorcet Loser 

Burial Invulnerability
Later-no-Harm
Later-no-Help

Mono-add-Top
Mono-add-Plump  (implied by mono-add-top)
Mono-append
Irrelevant Ballots

Clone-Winner
Clone-Loser  (together these two add up to Clone Independence)

As far as I can tell, the only real points of dissatisfaction with IRV in 
Australia are
(a) that in some jurisdictions the voter is not allowed to truncate (on pain of 
his/her
vote  being binned as invalid) and (b) that it isn't multi-winner PR so that 
minor
parties can be fairly represented.

I gather the Irish are also reasonably satisfied with it for the election of 
their President.

snip
I've really come to like Bucklin, because it allows voters to 
exercise full power for one candidate at the outset, then add, *if 
they choose to do so*, alternative approved candidates.
snip

The version of Bucklin Abd advocates (using ratings ballots with voters able to 
give
as many candidates they like the same rating and also able to skip slots) tends
to be strategically equivalent to Approval  but entices voters to play silly 
strategy
games sitting out rounds.

It would be better if 3-slot ballots are used, in which case it is the same 
thing as
(one of the versions of) Majority Choice Approval (MCA).

IMO the best method that meets  Favourite Betrayal (and also the best 3-slot 
ballot method)
is Strong Minimal Defence, Top Ratings:

*Voters fill out 3-slot ratings ballots, default rating is bottom-most
(indicating least preferred and not approved).

Interpreting top and middle rating as approval, disqualify all candidates
with an approval score lower than their maximum approval-opposition 
(MAO) score.
(X's  MAO score is the approval score of the most approved candidate on
ballots that don't approve X).

Elect the undisqualified candidate with the highest top-ratings score.*

Unlike MCA/Bucklin this fails Later-no-Help (as well as LNHarm) so the voters 
have a less
strong incentive to truncate.

Unlike MCA/Bucklin this meets Irrelevant Ballots. In MCA candidate X could be 
declared the
winner in the first round, and then it is found that a small number of voters 
had been wrongly
excluded and these new voters choose to openly bullet-vote for nobody (perhaps 
themselves
as write-ins) and then their additional ballots raise the majority threshold 
and trigger a second 
round in which X loses.

I can't take seriously any method that fails Irrelevant Ballots.

Compliance with Favourite Betrayal is incompatible with Condorcet. If you are 
looking for a 
relatively simple Condorcet method, I recommend Smith//Approval (ranking):

*Voters rank from the top candidates they approve. Equal-ranking is allowed. 
Interpreting being ranked above at least one other candidate as approval, elect 
the most 
approved member of the Smith set (the smallest non-empty set  S of candidates 
that pairwise
beat all the outside-S candidates).*


Chris Benham


  
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[EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws

[Chris Benham]

Dave Ketchum wrote (18 Jan 2010):

In response I will pick on LNH for not being a serious reason for  
rejecting Condorcet - that such failure can occur with reasonable  
voting choices for which the voter knows what is happening.  Quoting  
from Wikipedia:

For example in an election conducted using the Condorcet compliant  
method Ranked pairs the following votes are cast:
49: A
25: B
26: CB
B is preferred to A by 51 votes to 49 votes. A is preferred to C by  
49 votes to 26 votes. C is preferred to B by 26 votes to 25 votes.
There is no Condorcet winner and B is the Ranked pairs winner.
Suppose the 25 B voters give an additional preference to their  
second choice C.
The votes are now:
49: A
25: BC
26: CB
C is preferred to A by 51 votes to 49 votes. C is preferred to B by  
26 votes to 25 votes. B is preferred to A by 51 votes to 49 votes.
C is now the Condorcet winner and therefore the Ranked pairs winner.
By giving a second preference to candidate C the 25 B voters have  
caused their first choice to be defeated.


Pro-A is about equal strength with anti-A.  For this it makes sense  
for anti-A to give their side the best odds with the second vote  
pattern, not caring about LNH (B and C may compete with each other,  
but clearly care more about trouncing A).
snip

Dave,
Your assumption that  B and C may compete with each other, but clearly 
care more about trouncing A  is based on what?

The ballots referred to contain only the voters' rankings, with no indications
about their relative preference strengths.

If you read my entire post you will see that in it I endorse three methods,
one of which is a Condorcet method.

Chris Benham


  
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[EM] Strong Minmal Defense, Top Ratings

[Chris Benham]

In a recent EM post in another thread, I defined and recommended the
Strong Minimal Defense, Top Ratings method  (that I first proposed
in 2008) as the best of the methods that meet the Favourite Betrayal
criterion, and also the best 3-slot ballot method:

*Voters fill out 3-slot ratings ballots, default rating is bottom-most
(indicating least preferred and not approved).

Interpreting top and middle rating as approval, disqualify all candidates
with an approval score lower than their maximum approval-opposition 
(MAO) score.
(X's  MAO score is the approval score of the most approved candidate on
ballots that don't approve X).

Elect the undisqualified candidate with the highest top-ratings score.*

I gather from one off-list response that this sentence of mine could have
been more clear:

'Unlike MCA/Bucklin this fails Later-no-Help (as well as LNHarm) so the voters 
have a less
strong incentive to truncate..'

I neglected to mention that I think it is desirable that after top-voting X, 
ranking Y below X
(but above bottom) should be about equally likely to help X as to harm X.

This implies that if one of the the two LNhs are failed, it is desirable that 
the other is also.

MCA/Bucklin meets Later-no-Help while failing Later-no-Harm. The voters have a 
big incentive
to truncate, and to equal-rank at the top, so with strategic voters it tends to 
look like  plain Approval.

In SMD,TR after top-rating X, middle-rating Y may harm X or may help X.

As discussed in 2008, it fails Mono-add-Top  (and so Participation).

8: C
3: F
2: XF
2: YF
2: ZF

F wins after all other candidates are disqualified, but if  2 FC ballots are
added C wins.

Of course it is far from uniquely bad in that respect. A big plus for it is 
that it is virtually alone
in meeting my proposed  Unmanipulable Majority strategy criterion:

Regarding my proposed Unmanipulable Majority criterion:

*If (assuming there are more than two candidates) the ballot 
rules don't constrain voters to expressing fewer than three 
preference-levels, and A wins being voted above B on more 
than half the ballots, then it must not be possible to make B 
the winner by altering any of the ballots on which B is voted 
above A without raising their ranking or rating of B.*

http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023530.html

In common with MCA it meets mono-raise (aka ordinary monotonicity) and a 3-slot 
ballot version of
Majority for Solid Coaltions, which says that if  majority of the voters rate a 
subset S of the candidates
above all the outside-S candidates, the winner must come from S.


From the post that introduced SMD,TR:


It is more Condorcetish and has a less severe later-harm problem than MCA, 
Bucklin,
or  Cardinal Ratings (aka Range, Average Rating, etc.)

40: AB
35: B
25: C

Approval scores:    A40,   B75,   C25 
Approval Opp.:  A35,   B25,   C75
Top-ratings scores: A40,   B35,   C25 

They elect B, but SMD,TR elects the Condorcet winner A.


Chris Benham


  
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[EM] IRV vs Plurality

[Chris Benham]

Juho  wrote (25 Jan 2010):

I reply to myself since I want to present one possible simple method  
that combines Condorcet and added weight to first preferences  
(something that IRV offers in its own peculiar way).

Let's add an approval cutoff in the Condorcet ballots. The first  
approach could be to accept only winners that have some agreed amount  
of approvals. But I'll skip that approach and propose something  
softer. A clear approval cutoff sounds too black and white to me  
(unless there is already some agreed level of approval that must be  
met).

The proposal is simply to add some more strength to opinions that  
cross the approval cutoff. Ballot ABCD would be counted as 1 point  
to pairwise comparisons AB and CD but some higher number of points  
(e.g. 1.5) to comparisons AC, AD, BC and BD. This would introduce  
some approval style strategic opportunities in the method but basic  
ranking would stay as sincere as it was. I don't believe the approval  
related strategic problems would be as bad in this method as in  
Approval itself.
snip

The  some higher number of points (e.g. 1.5)  looks arbitrary and results
in the method failing Majority Favourite, never mind Condorcet etc.

51: ABC
41: BCA
08: CAB

BA 61.5 - 59,  BC 112.5 - 12,  AC 76.5 - 53

51% voted A as their unique favourite and 59% voted A above B, and yet B wins.

Chris Benham


  
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