Re: [EM] Statement by this list (was Remember toby Nixon)

[Juho Laatu]

On 27.5.2011, at 10.01, Jameson Quinn wrote:

> This thread, like this list, has two purposes - practical advocacy and 
> mathematical exploration.

One could divide the field also further by making a difference between 1) 
practical advocacy, 2) practical exploration of real life examples, 3) 
practical method exploration in general, and 4) mathematical (theoretical) 
exploration. These could mean respectively e.g. 1) active participation in 
politics, 2) using the current status of some country / election as a basis for 
the work, 3) general recommendations for presidential elections, and 4) 
delegation of one's vote to an intelligent computer in a future dystopia, or 
maybe just plain mathematical properties of some methods.

> 
> On the practical advocacy front, I'd propose a process:
> 0. We discuss get some degree of informal consensus on this process itself - 
> I imagine it will take about a week, so say, before Sunday June 5th.
> 1. We draw up a statement which details the serious problems with plurality 
> in the US context, and states that there are solutions. Leave a blank space 
> for a list of acceptable solutions. This statement, when finished (after step 
> 3) would be "signable" by any members of this list, completely at their own 
> option.

Good approach. I have one comment on the target statement. Expression "problems 
with plurality in the US context" contains the assumption that the traditional 
two-party system in not the correct solution for the US. Expression "and states 
that there are solutions" refers to possible solutions at some general and 
neutral level. This latter formulation is a theoretical statement that does not 
yet say what the US should do. This is interesting from the point of view that 
US citizens might want to say what the US should do in this question while the 
non-US-citizens might be happy with stating the theoretical facts and possible 
options only.

There could thus be two levels. One for practical advocation and political 
activism within some country and one for general opinions, coming from neutral 
experts (maybe unwilling to take position on the internal matters of that 
country). That is, category 1) vs. categories 2) and 3) in my list above.

> 2. We take a vote on what options to list. We can use betterpolls.com, 
> remembering that the scores there are -10 to 10, and negative/positive is 
> mapped to approval/disapproval.

Voting could be a more difficult process than collecting the list of options 
using sone "informal consensus" as in point 0. In general I tend to rely on 
some single person (or few) taking a leading role in creating such a paper that 
it can be agreed my some critical mass. One can also produce serially multiple 
versions of the list and paper to find the best combination (that the creators 
and as large group of supporters as needed are happy to sign).

> 3. We list the options and the winner(s) in the statement and sign it.
> 4. When we have a good number of signatures, we put out a "press" release to 
> some bloggers who've shown an interest in the issue (e.g. Andrew Sullivan)

Would "we" be the list of supporters? That sounds easier than using the name of 
this list.

> 
> My hope is that, despite the varied opinions, we could say something clearly 
> and strongly enough to have an impact.

I'm sure there are many points where most (or at least many credible) experts 
agree and that would bring useful information to politicians, practical 
reformers and regular voters. Maybe it would take some strong individual(s) 
dedicated to this kind of practical matters to extract those opinions out from 
the rest of the experts.

I'd be happy to see some general statements with wide consensus among experts 
on how the voting practices could be improved allover the world (i.e. also 
practical facts that can support real life decisions in addition to personal 
opinions and mathematical facts).

Juho


> 
> JQ
> 
> Election-Methods mailing list - see http://electorama.com/em for list info


Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] remember Toby Nixon?

[Jameson Quinn]

>
>
> If you are looking for simplicity then maybe also minmax should be
> considered since it (the margins version) simply measures the number of
> required additional voters to beat all others.


I agree. If minimax is twice as likely to be adopted, because it's simpler,
and gives >95% of the advantage vs. plurality of the theoretically-best
Condorcet methods, then it *is* the best. And besides, if we try to get
consensus on which is the absolutely best completion method, then almost by
definition, we're going to end up arguing in circles (cycles?).

JQ

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] Hybrid/generalized ranked/approval ballots

[Peter Zbornik]

Hi Kevin,

I am sending you a small hopefully clarifying P.S. to my email below.
1] My appologies for some unfinished sentences, please disregard them

2] In my email below I state three things:

a] Giving explicitly equally ranked candidates 0.5 votes each in their
pairwise comparison, but not for unranked candidates does not violate
Woodalls's plurality criterion in a condorcet election where winning
votes are used. Woodall's plurality criterion is only violated if symetrical
completion is used and the previously unranked candidates are given 0.5
votes each.

b] In order to preserve the power of the blank vote to prevent a candidate
from being elected in a Condorcet election, it is necessary to introduce a
blank vote criterion (static quota or absolute majority criterion),
which entails the following rule: in a Condorcet single winner election a
candidate wins a pairwise comparison only if he/she gets a majority of the
total votes cast (including blank votes).

c] combinations of the rules
(i) Rule b] can be combined with rule a] (winning votes) without violating
Woodall's plurality criterion.
(ii) Rule b] can be applied for winning rules: margins and quotas similarly
as for case (i) above
(iii) With losing votes I am not sure (haven't studied this criterion), but
I guess there should be a natural extension along the principles in (i)
above.

I hope this makes the email below somewhat clearer.

Best regards
Peter Zbornik

On Fri, May 27, 2011 at 7:35 PM, Peter Zbornik  wrote:

> Hi Kevin,
>
> I think an additional rule, "the absolute majority rule" is needed in
> Condorcet elections in order to preserve the power of a blank vote to block
> the election of a candidate and force new elections.
>
> This rule might be used "on top" of the winning votes rule and would
> require a candidate to get that more than 50% of the votes cast in order to
> get a win in a pairwise comparison in a Condorcet election.
>
> This extra rule, if combined with winning votes, would not violate Woodal's
> plurality criterion furthermore it would obey what I call the
>
> I think that the discussion so far was confounded by requiring equal
> treatment to two different "phenonema": (i) incomplete ballots (or partially
> blank votes as I would like to call them) and (ii) equally ranked
> candidates, where the ranking is explicitly made on the ballots.
>
> This leads to equal treatment between unranked candidates and explicitly
> ranked candidates with equal ranking.
>
> I propose different rules for:
> (i) unranked candidates on partially blank votes (incomplete ballots).
> (ii) equally ranked candidates, where the ranking is explicitly made on the
> ballot
>
> Rule (i) above applies for candidates not given any ranking on the ballot.
>
> Rule (ii), gives two explicitly equally ranked candidates 0.5 points each
> in a pairwise comparison.
> Rule (i) however a new winning rule (or maybe it has been proposed before)
> in order to preserve the majority criterion in condorcet elections with
> partially blank votes (incomplete ballots).
>
>  If we have the election
> 30 A>B
> 40 B>A
> 30 Blank,
> then in a condorcet election 
> (Schulze) B
> is elected, while in a majority election requiring 50 percent of the votes
> cast, no candidate is elected.
>
> Thus Schulze elections
>
> We can compare this situation with voting, where you can vote "yes", "no"
> and "abstain", in order to get the vote passed 50% of the votes cast are
> required to be "yes" votes.
> It might thus be appropriate to retain this blocking property of the
> abstention (or blank) vote for Condorcet elections.
>
> I think that the so far proposed winning criteria do not allow for
> abstention voting in condorcet elections.
>
> I guess that the only way to retain the expressive power of the blank vote,
> is through adding an additional rule for when a pairwise comparison
> to qualifies as a win.
>
> This rule would state that a pairwise comparison results in a win only if
> the candidate gets more than 50% of all votes cast in the election.
>
> Thus in the election
>  40 A>B
> 30 B>A
> 40 Blank
> A vs B would end 30% vs 40%.
> No candiate would win.
> New elections would be held.
> Maybe this rule could be called the "absolute majority" rule for instance
> (or whatever).
>
>  I.e. winning votes, losing votes, ratio and margins do not respect the
> something we might call the "blank vote criterion" or the "static quota
> criterion", which for single winner elections states that: a candidate can
> win a two-candidate election only if he/she is preferred by a majority of
> the voters".
>
> The general case of the "blank vote criterion" or the "static quota
> criterion" would read: a candidate can win a multiple member election only
> if he/she is preferred by a static quota number of the voters" (the quota
> used can be Droop, Hare, etc.).
>
> However, in order not to penalize explicit equal rankings on the ballot by
> givin

Re: [EM] Hybrid/generalized ranked/approval ballots

[Peter Zbornik]

Hi Kevin,

I think an additional rule, "the absolute majority rule" is needed in
Condorcet elections in order to preserve the power of a blank vote to block
the election of a candidate and force new elections.

This rule might be used "on top" of the winning votes rule and would require
a candidate to get that more than 50% of the votes cast in order to get a
win in a pairwise comparison in a Condorcet election.

This extra rule, if combined with winning votes, would not violate Woodal's
plurality criterion furthermore it would obey what I call the

I think that the discussion so far was confounded by requiring equal
treatment to two different "phenonema": (i) incomplete ballots (or partially
blank votes as I would like to call them) and (ii) equally ranked
candidates, where the ranking is explicitly made on the ballots.

This leads to equal treatment between unranked candidates and explicitly
ranked candidates with equal ranking.

I propose different rules for:
(i) unranked candidates on partially blank votes (incomplete ballots).
(ii) equally ranked candidates, where the ranking is explicitly made on the
ballot

Rule (i) above applies for candidates not given any ranking on the ballot.

Rule (ii), gives two explicitly equally ranked candidates 0.5 points each in
a pairwise comparison.
Rule (i) however a new winning rule (or maybe it has been proposed before)
in order to preserve the majority criterion in condorcet elections with
partially blank votes (incomplete ballots).

 If we have the election
30 A>B
40 B>A
30 Blank,
then in a condorcet election
(Schulze) B
is elected, while in a majority election requiring 50 percent of the votes
cast, no candidate is elected.

Thus Schulze elections

We can compare this situation with voting, where you can vote "yes", "no"
and "abstain", in order to get the vote passed 50% of the votes cast are
required to be "yes" votes.
It might thus be appropriate to retain this blocking property of the
abstention (or blank) vote for Condorcet elections.

I think that the so far proposed winning criteria do not allow for
abstention voting in condorcet elections.

I guess that the only way to retain the expressive power of the blank vote,
is through adding an additional rule for when a pairwise comparison
to qualifies as a win.

This rule would state that a pairwise comparison results in a win only if
the candidate gets more than 50% of all votes cast in the election.

Thus in the election
 40 A>B
30 B>A
40 Blank
A vs B would end 30% vs 40%.
No candiate would win.
New elections would be held.
Maybe this rule could be called the "absolute majority" rule for instance
(or whatever).

 I.e. winning votes, losing votes, ratio and margins do not respect the
something we might call the "blank vote criterion" or the "static quota
criterion", which for single winner elections states that: a candidate can
win a two-candidate election only if he/she is preferred by a majority of
the voters".

The general case of the "blank vote criterion" or the "static quota
criterion" would read: a candidate can win a multiple member election only
if he/she is preferred by a static quota number of the voters" (the quota
used can be Droop, Hare, etc.).

However, in order not to penalize explicit equal rankings on the ballot by
giving both equally ranked candidates 0 wins thus making it more difficult
for these candidates to meet the "static quota criterion", separate
treatment is needed for explicit equal rankings and for candidates left out
of the ballot, in the same way as I propose these two cases to be separately
treated in an IRV-STV election.

Thus we need to add two new rules to a Condorcet election.

*The generalized symmetric completion rule for condorcet elections:*
*Equal rankings explicitly made on the ballot are counted as 0.5 win for
each candidate.*

 Any candidate left out from the ballot is counted as ranked lower than all
candidates explicitly ranked on the ballot. This rule is currently
implemented for Schulze, so I just state it for completenes.

*Absolute majority rule: a pairwise comparison between two
candidates results in a win only if more than 50% of the total votes cast
are in favour of any candidate.*
**
The absolute majority rule might thus lead to the case where there is no
winner of the election.

In that case a new election might be held, or the voters can go home.

It seems most natural to combine the absolute majority rule with winning
votes, but in theory it might maybe be combined with any other rule
(margins, ratios, losing votes). I have no firm oppinion on this.

Turning to your example to apply these new rules:
35 A>B
25 B
40 C

Let us first count the votes cast.
 Total votes cast are 100 with the following matrix:
X   AB   C
A   X35  35
B   25X  60
C   40  40  X
We only count as a win >50% of the votes casts.
Thus the election results in no candidate being elected as no candidate
scores a win against bo

Re: [EM] Hybrid/generalized ranked/approval ballots

[Kevin Venzke]

Hi Peter,
 
Let me say first of all that proportional representation isn't my area of 
interest, so you
shouldn't take anything I say to apply also to a PR situation.
 
And although STV has a single-winner case, my thoughts on equal ranking don't 
apply
there either.

 


--- En date de : Ven 27.5.11, Peter Zbornik  a écrit :

[end quote]

I think you forgot Schulze as it is usually done: Weakest biggest loss.


 
With "weakest biggest loss", do you mean losing votes 
(http://m-schulze.webhop.net/, page 7)?
 
 
No I mean "winning votes" on that page. Is that what you meant by "biggest win"?
I can't really see how those could be the same thing.

 

Experimentally, in simulations: When you treat equal-ranking as split
votes, voters will have to compromise more often, instead of just
compressing the top ranks. This suggests weaker, non-frontrunner
candidates are more likely to be best advised to drop out of the race,
because their presence is more likely to harm the voters that support
them.

 
Could you please send me a link to these simulations?
 
 
There is no complete set of simulations currently/yet. If you want to get a 
sense of
what I was doing, you can go to the archives:
http://lists.electorama.com/pipermail/election-methods-electorama.com/
and read my March 2011 posts in particular. My simulations involve voters who 
do not
initially know anything about the method except the valid ballot types, but try 
to 
determine their ideal vote in a given situation via repeated and hypothetical 
polling.
 
I have explained (probably five years ago) why we should expect margins to have 
more
favorite betrayal incentive than WV though. Suppose that you want to vote A>B, 
but
so doing causes C to win instead of B, because A defeats B pairwise. In WV both
reversing the order to be B>A or compressing the top to be A=B have the same 
effect
in reducing the magnitude of B's loss to A. But in margins reversal is twice as 
effective
as compression.
 
Kevin Venzke
 
Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] Hybrid/generalized ranked/approval ballots

[Peter Zbornik]

Kristoffer,

just a small P.S. to my email below.

Maybe the problems with the incomplete ballots and dynamic quotas below have
something to do with electing a fixed number of seats.
That's just a hunch.

I think you mentioned that a variable number of seats might give better
proportional representation than a fixed number.

However electing a variable number of seats will probably have little
political support in my party, so this question is more a question out of
curiousity.

Peter

On Fri, May 27, 2011 at 12:28 PM, Peter Zbornik  wrote:

> Hi Kristoffer,
>
> answers in the text of your email below.
>
> For the Czech Green party, we might get some STV elections (probably
> IRV-STV, maybe Meek-STV) for some of the party councils encoded in our
> statutes by the end of this year.
>
> For now, proportional party list elections, ranked proportional council
> elections and condorcet based elections seem to be out of the picture for
> now, as the interest is too low.
>
>  For information: ranked proportional party lists are used by at least
> the Scottish greens, the English greens and the UK Liberals in at least some
> elections.
> I can send some references to their statutes, in case anybody is
> interested.
>
> STV in green political parties seems to be exclusively used only in
> anglo-saxon countries, where it is used rather often.
>
> Best regards
> Peter Zborník
>
>
>  On Thu, May 26, 2011 at 8:00 PM, Kristofer Munsterhjelm <
> km_el...@lavabit.com> wrote:
>
>
>> Peter Zbornik wrote:
>>
>>
>>> Dear all,
>>>  Please let me return to an older discussion (see emails below).
>>> The issue of the hybrid ballot A>B=C>D.
>>> Just an idea on this topic, which might be worth mentioning.
>>> It could be a way to handle the problem of bullet voting.
>>> Ant it could be a way to disband the dichotomy between different
>>> criterias of winning in condorcet elections (margins, winning votes, quotas
>>> losing votes).
>>>  1] IRV-based elections:
>>> Basically in IRV-based STV, when arriving at an equal sign in the ballot,
>>> the ballot could simply be split into the number of candidates with equal
>>> preferences and re-weighted accordingly (i.e. for instance A=B=C would give
>>> three ballots, A>B=C, B>A=C, C>A=B, each with weight 1/3 of the original
>>> weight).
>>>
>>>
>>
>> This sounds a lot like Woodall's concept of "symmetric completion". A
>> method passes symmetric completion if truncated ballots are split into
>> ballots with the latter (truncated) preferences filled out, for all possible
>> ways those can be filled out, and with the same cumulative power. E.g. with
>> candidates A,B,C,D and a method satisfying symmetric completion,
>>
>> 1: A>B
>>
>> is the same as
>>
>> 0.5: A>B>C>D
>> 0.5: A>B>D>C.
>>
>> Unless I'm mistaken, you're generalizing symmetric completion to
>> equal-rank.
>>
>>
>
> Yes, I am generalizing symmetric completion to equal rank.
> Unlike Woodal my proposal is computable for a large number of candidates in
> IRV based STV elections.
>
>  If we wanted to perform symmetric completion according to Woodall and if
> we would have, say seventeen candidates, who were equal-ranked, then for
> each ballot, we would need to generate 17!=355.687.428.096.000
> strictly-ranked ballots in order to exhaust all permutations, which is not
> computationally feasible.
>
> Example an IRV-STV election: A=B=C would according to Woodall be broken
> down into 3!=6 ballots: ABC, ACB, BAC, BCA, CAB, CBC.
>
> I propose that the ballot to be broken down into 3 ballots: A>B=C, B>A=C,
> C>A=B, which is nicely computable and the result is the same as Woodalls
> proposal for IRV-STV elections.
>
> Maybe the reason why equally ranked ballots aren't used in STV elections
> might be that a computable solution hasn't  explicitly been given.
>
> The issue of a truncated ballot (incomplete ballot or partially blank
> ballot) is different from the treatment of equally ranked candidates.
>
>
>> Woodall writes about symmetric completion here:
>> http://www.votingmatters.org.uk/ISSUE3/P5.HTM , where he also shows that
>> STV does not obey that criterion, but that IRV does. In another Voting
>> Matters article (http://www.votingmatters.org.uk/ISSUE14/P1.HTM ), he
>> shows how STV can be made to obey symmetric completion, but says that doing
>> so isn't a good idea.
>>
>
> It seems that this is a matter of taste.
> The authors argue for their criterion based on one example.
> I do not find the example convincing, since when adding a candidate with a
> large number of additional votes in an STV election, then we have a
> different electorate which should be differently proportionally represented.
>
> After reading the articles above, I've come to think that the issue boils
> down to how to handle blank votes.
> The issue is not as clear-cut as I thought :o)
>
>  Weather one accepts the plurality criterion really depends on the
> preferred treatment of incomplete ballots, or partially blank ballots as I
> would rather call them.

Re: [EM] Hybrid/generalized ranked/approval ballots

[Peter Zbornik]

Hi Kevin,

answers and questions in the text of your email below.

Best regards
Peter Zborník

On Thu, May 26, 2011 at 5:12 PM, Kevin Venzke  wrote:

> Hi Peter,
>
> You are right. Your treatment has been discussed for, I suppose, 15+ years
> on this list, and your reasoning for it is a major factor.
>
> --- En date de : Jeu 26.5.11, Peter Zbornik  a écrit :
> Kevin Venzke wrote in his mail below (May 9th 2010):
> 35 A>B
> 25 B
> 40 C
> A will win. This is only acceptable when you assume that the B and C
> voters meant to say that A is just as good as the other candidate that
> they didn't rank. I don't think this is likely to be what voters expect.
> It seems misleading to even allow truncation as an option if it's treated
> like this.
> End of quote
>
> you wrote:
> Well I think think that as a voter I would indeed be pleased if A would win
> and not C.
> If the completion system above would be used (i.e. A=B would be counted as
> 0.5 win for A vs B and 0.5 win for B vs A), then there the winner would
> always be the same disregarding which of the following winning criteria was
> used: winning votes, losing votes, margins or quotas.
>
> [end quote]
>
> Can you explain why as a voter you would be pleased if A won and not C?
> What reason do these ballots give us to suppose that A is a better
> candidate than C? Does the fact that A voters have a second preference
> make A a better candidate?


I aggree that the issue of incomplete ballots or partially blank votes as I
would call it, is not as clear cut as I thought in the post above. Please
refer to the discussion in the email to Kristoffer.


>
> In other words: Electing A violates Woodall's Plurality criterion.


I aggree.

>
> I don't find the election of C to be very good, but it is better than
> electing A.
>
>
> [resume quote]
> Let us analyse the example in your mail below. We apply the Schulze
> beatpath with different criteria (biggest win, margins and ratios):
> [end quote]
>
> I think you forgot Schulze as it is usually done: Weakest biggest loss.
>

With "weakest biggest loss", do you mean losing votes (
http://m-schulze.webhop.net/, page 7)?


> In that case you elect B, which is my preference. This minimizes the
> number of voters who feel the outcome was spoiled by one of the
> candidates.
>
>
> [resume quote]
> What are the pros and cons of the approach above?
> Prima facie it seems that the treatment of hybrid ballots above could solve
> the problem of bullet voting, but I am far from sure.
> [end quote]
>
> I still stand by what I originally said, that I don't believe voters will
> expect or like this treatment of truncation. Voters will expect that if
> more than half of the voters say X was better than Y, then that's the
> important contest, and Y should certainly not win. The presence of some
> weak candidate Z should not cause the method to be confused about X vs.
> Y.
>

Yes, that depends if the voters think Woodall's plurality criterion is
important. I think the goal of STV elections should be proportional
representation, which might (or might not) be hampered by the plurality
criterion. See the discussion in my response to Kristoffer's email.


>
> You will tell them you're only doing this for their own good. But I
> think there is an incurable disconnect between what truncation seems to
> mean and what it actually does mean in your scheme. I think that when
> you use this scheme, truncation should not be allowed at all: You should
> have to explicitly rank all the worst candidates equal, if that's how
> it's going to count.
>
> Otherwise, you are going to sometimes be electing candidates on the basis
> of equal rankings that were cast in the form of voters completely ignoring
> a candidate. That seems like an opportunity to criticize the legitimacy
> of the winner.


With this I do aggree.

>
> Experimentally, in simulations: When you treat equal-ranking as split
> votes, voters will have to compromise more often, instead of just
> compressing the top ranks. This suggests weaker, non-frontrunner
> candidates are more likely to be best advised to drop out of the race,
> because their presence is more likely to harm the voters that support
> them.
>

Could you please send me a link to these simulations?


>
> Kevin
>
>

Election-Methods mailing list - see http://electorama.com/em for list info

Re: [EM] Hybrid/generalized ranked/approval ballots

[Peter Zbornik]

Hi Kristoffer,

answers in the text of your email below.

For the Czech Green party, we might get some STV elections (probably
IRV-STV, maybe Meek-STV) for some of the party councils encoded in our
statutes by the end of this year.

For now, proportional party list elections, ranked proportional council
elections and condorcet based elections seem to be out of the picture for
now, as the interest is too low.

 For information: ranked proportional party lists are used by at least
the Scottish greens, the English greens and the UK Liberals in at least some
elections.
I can send some references to their statutes, in case anybody is interested.

STV in green political parties seems to be exclusively used only in
anglo-saxon countries, where it is used rather often.

Best regards
Peter Zborník


On Thu, May 26, 2011 at 8:00 PM, Kristofer Munsterhjelm <
km_el...@lavabit.com> wrote:


> Peter Zbornik wrote:
>
>
>> Dear all,
>>  Please let me return to an older discussion (see emails below).
>> The issue of the hybrid ballot A>B=C>D.
>> Just an idea on this topic, which might be worth mentioning.
>> It could be a way to handle the problem of bullet voting.
>> Ant it could be a way to disband the dichotomy between different criterias
>> of winning in condorcet elections (margins, winning votes, quotas losing
>> votes).
>>  1] IRV-based elections:
>> Basically in IRV-based STV, when arriving at an equal sign in the ballot,
>> the ballot could simply be split into the number of candidates with equal
>> preferences and re-weighted accordingly (i.e. for instance A=B=C would give
>> three ballots, A>B=C, B>A=C, C>A=B, each with weight 1/3 of the original
>> weight).
>>
>>
>
> This sounds a lot like Woodall's concept of "symmetric completion". A
> method passes symmetric completion if truncated ballots are split into
> ballots with the latter (truncated) preferences filled out, for all possible
> ways those can be filled out, and with the same cumulative power. E.g. with
> candidates A,B,C,D and a method satisfying symmetric completion,
>
> 1: A>B
>
> is the same as
>
> 0.5: A>B>C>D
> 0.5: A>B>D>C.
>
> Unless I'm mistaken, you're generalizing symmetric completion to
> equal-rank.
>
>

Yes, I am generalizing symmetric completion to equal rank.
Unlike Woodal my proposal is computable for a large number of candidates in
IRV based STV elections.

 If we wanted to perform symmetric completion according to Woodall and if we
would have, say seventeen candidates, who were equal-ranked, then for each
ballot, we would need to generate 17!=355.687.428.096.000 strictly-ranked
ballots in order to exhaust all permutations, which is not computationally
feasible.

Example an IRV-STV election: A=B=C would according to Woodall be broken down
into 3!=6 ballots: ABC, ACB, BAC, BCA, CAB, CBC.

I propose that the ballot to be broken down into 3 ballots: A>B=C, B>A=C,
C>A=B, which is nicely computable and the result is the same as Woodalls
proposal for IRV-STV elections.

Maybe the reason why equally ranked ballots aren't used in STV elections
might be that a computable solution hasn't  explicitly been given.

The issue of a truncated ballot (incomplete ballot or partially blank
ballot) is different from the treatment of equally ranked candidates.


> Woodall writes about symmetric completion here:
> http://www.votingmatters.org.uk/ISSUE3/P5.HTM , where he also shows that
> STV does not obey that criterion, but that IRV does. In another Voting
> Matters article (http://www.votingmatters.org.uk/ISSUE14/P1.HTM ), he
> shows how STV can be made to obey symmetric completion, but says that doing
> so isn't a good idea.
>

It seems that this is a matter of taste.
The authors argue for their criterion based on one example.
I do not find the example convincing, since when adding a candidate with a
large number of additional votes in an STV election, then we have a
different electorate which should be differently proportionally represented.

After reading the articles above, I've come to think that the issue boils
down to how to handle blank votes.
The issue is not as clear-cut as I thought :o)

 Weather one accepts the plurality criterion really depends on the preferred
treatment of incomplete ballots, or partially blank ballots as I would
rather call them.

In order to guarantee to get all seats elected in an STV elections, it seems
that four different treatments of partially blank votes are possible:
1] the symmetrical completion, which is equivalent to requiring all voters
to rank all candidates as Kevin pointed out.
2] dynamic (or shrinking) quotas based on the number of active votes.
3] the candidate X: "none of the above" and new election if "none of the
above" is elected (http://en.wikipedia.org/wiki/None_of_the_above)
4] some seats simply are not elected (using static quotas). A new election
is held for the remaining seats.

Option three is used in the UK green party and possibly in other green
parties.
Personally I think that the blank vote s

Re: [EM] Remember toby Nixon

[Jameson Quinn]

On the mathematical-exploration side of things:

2011/5/26 

>
>
> > From: Kevin Venzke
> > To: election-meth...@electorama.com
> > Subject: Re: [EM] remember Toby Nixon? FS
> > Message-ID: <404845.50771...@web29613.mail.ird.yahoo.com>
> > Content-Type: text/plain; charset=iso-8859-1
> >
> > Hi Forest,
> >
> > --- En date de?: Mer 25.5.11, fsimm...@pcc.edu
> > a ?crit?:
> > > The main problem is determining (through the disinformation
> > > noise) who the front runners really are.
> > > Suppose the zero-information front runners to be candidates
> > > A and B, but that the media created front
> > > runners are C and D.? If everybody votes for one of
> > > these two falsely advertised front runners, then they
> > > become the front runners, but only through self fulfilling
> > > prophecy.
> >
> > The difference between Approval and Plurality here is that in
> > Pluralitywhen the frontrunners are A and B, generally only A and
> > B can win. Under
> > Approval it is not guaranteed that the winner will be one of these
> > candidates, as long as C or D haven't dropped out of the race.
> > If the perceived frontrunners are actually the worst candidates, any
> > better candidates should receive a vast number of votes.
> >
> > If C or D are clones of A/B then I think they probably would
> > drop out
> > of the race. But if we are simply electing the wrong clone, that
> > doesn'tseem like an enormous problem.
> >
>
> Yes, Approval is much better than Plurality and quickly homes in on the CW
> if there is one.  But this
> homing in typically takes a couple iterations, which doesn't help when the
> candidates change every four
> years.
> 
> Election-Methods mailing list - see http://electorama.com/em for list info
>

I suspect that Approval, with even a modicum of openly-reported polling,
would mostly get the CW (pairwise champion) on the first try... and that,
given (real-world, perhaps-misguided, attempts at) strategy, actual
Condorcet methods would not do measurably better at this.

The one case where approval could fail to find the CW, even after a number
of iterations, is when there are two near-clones splitting/sharing a
majority (call them A1 and A2, and their strongest opponent B), and a "game
of chicken" between the supporters of those two. If A1 and A2 have similar
levels of support, the winner between those two will not be the CW, but
rather whichever of the two has more-strategic supporters. But if there are
too many such strategists, B will win. There is no dominant equilibrium to
this game.

DYN helps to resolve this somewhat, because it shifts the game of chicken
from an impossible-to-coordinate mass, secret-ballot election to the two
individual candidates themselves. This makes it much less likely that B will
win by mistake; but it does not ensure that the winner between A1 and A2
will be the CW.

It is possible to patch this problem with DYN by using some measure of
candidate quality from the first, and only allowing candidates to "approve"
of other candidates of higher quality. This is in the spirit of IRV's
elimination-and-transfer, and like that process, it is theoretically
vulnerable to center squeeze. However, I think that it would be possible to
use a measure of candidate quality such that the overwhelming probability
would be that the highest-quality candidate by that measure would be the CW,
and that exceptions would be minor and/or manageable through simple
strategies by the candidates. The measure I'd pick would be the range score
of the candidate, measuring preference (circled), approved, and [unmarked or
unapproved], as 2, 1, 0 respectively. (I'm grouping unmarked and unapproved
so that there is no strategic motivation to explicitly unapprove a
near-clone of your favorite candidate. Note that this 2,1,0 range score,
unlike any more-finely-chopped range score, has the property that the actual
CW is guaranteed to have a range score as high or higher than the highest
approval score.)

So, translated into ordinary language:

"You circle your favorite candidate, and approve or disapprove of as many
other candidates as you want. Your favorite candidate is automatically
counted as both favorite and approved. After these results are published,
your favorite candidate may 'fill in your ballot' by approving of any other
candidate who has more favorites plus approvals than themself. If you had
left any such candidates unmarked, they then get a vote for you. The
candidate with the most approvals wins."

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[EM] Statement by this list (was Remember toby Nixon)

[Jameson Quinn]

This thread, like this list, has two purposes - practical advocacy and
mathematical exploration.

On the practical advocacy front, I'd propose a process:
0. We discuss get some degree of informal consensus on this process itself -
I imagine it will take about a week, so say, before Sunday June 5th.
1. We draw up a statement which details the serious problems with plurality
in the US context, and states that there are solutions. Leave a blank space
for a list of acceptable solutions. This statement, when finished (after
step 3) would be "signable" by any members of this list, completely at their
own option.
2. We take a vote on what options to list. We can use betterpolls.com,
remembering that the scores there are -10 to 10, and negative/positive is
mapped to approval/disapproval.
3. We list the options and the winner(s) in the statement and sign it.
4. When we have a good number of signatures, we put out a "press" release to
some bloggers who've shown an interest in the issue (e.g. Andrew Sullivan)

My hope is that, despite the varied opinions, we could say something clearly
and strongly enough to have an impact.

JQ

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