Re: [EM] Simulation of Duverger's Law

2008-10-17 Thread Raph Frank
On Fri, Oct 17, 2008 at 12:44 AM, Kevin Venzke [EMAIL PROTECTED] wrote:
 I think what we need to see, are IRV elections to a chamber that is
 not parliamentary (i.e. there is no particular prize for one party getting
 the most seats). Perhaps in that situation IRV could support more than
 two parties.

In Ireland, the rule is that the Taoiseach (PM) needs to obtain the
support of a majority of the Dail before he is appointed.  This seems
pretty fair.  There is no specific incentive to obtain the most seats
(parties can always form a coalition later).

However, it looks like in (nearly?) all other parliamentary countries,
the rule is that the leader of the largest party is appointed.  The
eliminates the need to form a coalition.

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Re: [EM] Strategic Voting and Simulating It

2008-10-17 Thread Raph Frank
On Fri, Oct 17, 2008 at 1:32 AM, Kevin Venzke [EMAIL PROTECTED] wrote:
 Hi Raph,

 --- En date de : Jeu 16.10.08, Raph Frank [EMAIL PROTECTED] a écrit :
 I think Warren has some simulations where the voters are
 spread over
 1-2 axes.  (He can comment).  My understanding is that
 there are lots
 of different distributions.

 Ok. That is better. But you still have the problem that it's open to
 endless debate, what exactly the realistic simulation method is.

Right, Warren's proposal is to try lots of different variations.  A
method that scores best under lots of different assumptions is likely
to be best.

Ofc, even then, he may not have covered enough search space.

 But this ignores the fact that parties still want to try to win the
 election. If they back candidates at random, they could conceivably hold
 on to frontrunner positions, but they wouldn't generally win, so they
 don't do this.

One option here is to do what parties actually do and hold a plurality primary.

In fact, lots of different primaries election types could be tested.

 It is still a problem to take this interpretation of FPP as a starting
 principle to measure *all* rank ballot methods.

The advantage is that it can be easily applied to voters with random utility.

It automatically splits them into 2 groups.

 I am not sure I've seen the other thread but I'll look for it.

It was the suggestion that you pick 2 candidates as the top 2 and then
test if it is stable by allowing each voter to change his vote one at
a time.

 Perhaps... I've never written a simulation to study nomination incentive
 specifically, but I have written e.g. a FPP simulation, in which
 voters stop voting for a candidate (in the polls leading up to the
 election) when the calculated benefit to the vote disappears. And in
 FPP there is no way for the benefit to come back (in contrast to, say,
 Approval, which in my simulations of the same sort had the potential to
 never arrive at stability).

If there isn't a condorcet winner, then you get instability.  I
remember running sims on the Rank your favourite of the top 2 and all
you like better strategy and it is unstable, if there isn't a clear
condorcet winner.  This is a representation of approval's condorcet
seeking behaviour.

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Re: [EM] Populism and Voting Theory

2008-10-17 Thread Michael Allan
Greg Nisbet wrote:
 Which system would be the most bang for the buck? What system would take the
 least amount of convincing for the greatest gain?
 ... 
 Which system do you think would work best that is actually achievable?

Don't forget cascade voting, because:

  a) cost = zero bucks

  b) no need to convince voters up front (they can just try it out),
 nor get approval from government nor parties (they have no say)

  c) actually achievable, because we're doing it now (but yet to prove
 popularity)

  d) works best in theory, so I think (but, again, yet to prove)

  http://zelea.com/project/votorola/home.xht

Anyway, it's something different to consider.

-- 
Michael Allan

Toronto, 647-436-4521
http://zelea.com/


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Re: [EM] Range Condorcet (No idea who started this argument, sorry; I am Gregory Nisbet)

2008-10-17 Thread Raph Frank
On Thu, Oct 16, 2008 at 3:17 AM, Greg Nisbet [EMAIL PROTECTED] wrote:
 This is called Cardinal Condorcet or something like that and is detailed
 here: http://fc.antioch.edu/~james_green-armytage/cwp13.htm

This is interesting.

I am unsure why the voter has to submit both a ranked list and a rated
ballot, especially since they have to be consistant with each other.
Surely, the rankings can be inferred from the ratings.

I guess some voters might just want to cast a rankings ballot and be
done with it.  In that case, they can just rate 9-8-7-6-5-4 ...
(though it does mean that they have to reverse order from a normal
ranking ballot).

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Re: [EM] Populism and Voting Theory

2008-10-17 Thread Raph Frank
On Fri, Oct 17, 2008 at 2:09 PM, Brian Olson [EMAIL PROTECTED] wrote:
 That's like asking the oft asked question, 'which candidate is electable?'
 and I HATE that question.
 It's like suggesting that we prematurely compromise and compress our
 election reform advocacy down to a single method to push for when I'd much
 rather say that I support: 1. IRNR, 2. Condorcet, 3. IRV, 4. Approval. And
 sometimes I want a side of PR-STV, redistricting and elimination of bad
 voting machines.

That is a good point, for a group that all accepts plurality is bad,
it is still in effect used for polling purposes.

I would probably go

1: Approval (slightly ahead of condorcet)
1: Condorcet
2: IRNR
3. IRV

I don't think IRNR is sufficiently examined to really know where to
put it though.  It might have serious strategy issues.

Anyway, you would rank PR-STV behind single winner election methods?

I would rate PR-STV as one of, if not the best voting system (and
certainly one of the best system that is actually in use).  It also
has the added advantage that it is also a redistricting reform (or at
least makes redistricting less important).

CPO-STV (or maybe Schulze-STV) are obvious improvements, but with big
costs in complexity.  I do think that vote management is a weakness of
PR-STV (I wonder if Schulze STV would stop parties bothering to try).
Also, the district sizes need to be reasonable (say 5+).  In Ireland,
there are 3.86 seats per constituency on average, which I think is to
low.

Also, if you could make one change, would you implement IRNR or
redistricting reform?  Unfortunately, with extreme gerrymandering, I
think most methods would still elect a member of one of the two
parties.

 In my few years of election reform advocacy, nearly everyone I've talked to
 agrees that 'rankings ballots' or 'ranked choice voting' is a good idea.
 Probably 80-90% of people I talk to I've been able to convince that IRV is
 severely suboptimal (but better than nothing) and that Condorcet methods are
 better. Maybe I should try to write down the elevator pitches/stump
 speechs/good lines/patter that seem to work and put together a pamphlet for
 election reform advocates.

Can't hurt.

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Re: [EM] Worst Voting Method

2008-10-17 Thread 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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Re: [EM] Range Voting vs Condorcet (Greg Nisbet)

2008-10-17 Thread Jobst Heitzig

Dear Diego,

you wrote:

 The risk of minority will remains. How does FAWRB perform in binary issues?


What you mean by risk of minority? That a minority favourite may win? 
Well, that is just the *feature* of FAWRB: It gives each part of the 
electorate full control over an equal share of the winning probability. 
This is the requirement of democracy.


So, when 55% prefer A and 45% prefer B and both groups do not care to 
look for a good compromise C or do not cooperate in electing such a good 
compromise by using FAWRBs cooperation mechanism, then indeed A will win 
with 55% probability and B will win with 45% probability - which is just 
fair and what a democratically thinking person would expect. This also 
answers your question about the binary case.


However, let me point out that in most real-world issues, there is a 
possibility to come up with a good compromise option.


Sometimes, for example, this can be achieved by side payments, that 
is, C is A plus some payments (or other forms of compensation) from the 
A supporting group to the B supporting group.


Once a good compromise is found, using FAWRB makes it probable that this 
compromise is also elected. Majoritarian methods fail here since with 
them, the majority has no incentive at all not to bullet vote for A and 
thus overrule the rest.


If a consensus exists between the factions, then this danger would be 
too rare. There`s no gain for any faction to leave the issue undecided.


I don't think so. In my experience of politics it is often the case that 
one faction strongly wants to stick with the status quo, so they would 
have a strong incentive to refuse cooperation under your scheme.



Not always we can find an unanimity...


Yes, that's exactly the reason why sometimes we need to resort to a 
chance process in order to give every voter their fair right to 
influence the decision.


Yours, Jobst


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Re: [EM] Populism and Voting Theory

2008-10-17 Thread Raph Frank
On Fri, Oct 17, 2008 at 3:29 PM, James Gilmour [EMAIL PROTECTED] wrote:
 Raph Frank   Sent: Friday, October 17, 2008 2:45 PM
 Anyway, you would rank PR-STV behind single winner election methods?

 This is an illogical question.  By definition, single winner elections 
 methods are for electing single winners.  By definition
 PR-STV is for obtaining proportionality of the voters for which several 
 winners must be elected together.  So you are not
 comparing like with like.

Fair enough, I meant would you elect a legislature via single winner or PR.

 Single winner voting systems should, of course, be used only for 
 single-office elections, like city mayor or state governor.  Single
 winner voting methods should never be used to elect assemblies, like a city 
 council or a state legislature.

Ok, then we are in agreement.

Actually, I would see the reviewing House of the legislature as less
important in this regard, but the primary/government linked House
should be PR based.

 There is, of course, a separate debate about the nature of assemblies elected 
 by PR voting systems (of different kinds) and those
 elected by single-winner voting systems.  But that is essentially a political 
 debate about how representative or how distorted you
 want the assembly to be, and about some of the other effects of some 
 single-winner voting systems, such as the tendency of some
 single-winner voting systems to manufacturing single-party majorities within 
 the assembly even when no such majority exists among
 the voters.  Some see such distortion of the voters' wishes as highly 
 undesirable, while others see that distortion as highly
 desirable, indeed, as an essential feature of the political system for good 
 and effective government.

True, some see the solid majorities given by plurality as one of its
main benefits.

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Re: [EM] Range Voting vs Condorcet (Greg Nisbet)

2008-10-17 Thread Raph Frank
On Thu, Oct 16, 2008 at 7:58 PM, Jobst Heitzig [EMAIL PROTECTED] wrote:
 The thing is that in such a case, it isn't really a single 'demos'. It is
 two groups voting as one.

 Do you mean to say democracy is only for societies which are
 sufficiently homogeneous?

To a certain extent, I would say it works reasonably if one faction is
75% or no faction is more than 1/3.

In the first case, the majority should be sufficiently confident in
its power that it doesn't have to be oppressive and in the second
case, there is a requirement for negotiation.

It also works if there is trust/good relations between the factions,
no matter the distribution.

Where is breaks down is when one group is a majority but not an
unassailable one.  If one group is 55-60%, then it needs to stay
together or it risks losing control.  This is made even worse if there
is distrust/fear between the two groups.  In Nothern Ireland, they
have a substantial minority who don't want NI to exist.

It also tends to move power to the leadership of the majority and away
from their supporters.

 You can still have compromises.

 Only if the majority for some reason prefers to elect the compromise
 than their favourite. But in that it seems the favourite was just not
 the true favourite of the majority but the compromise was. So, still the
 minority has no influence on the decision but can only hope that the
 majority is nice enough to decide for the compromise.

I was thinking of PR + negotiations in the legislature.  If a party
supports policy A in exchange for policy B being killed, and then the
other party breaks its word, then that is bad for that party's
reputation.  This will make it more difficult for it to make deals in
the future.

 In fact, it can be helpful if multiple issues are voted as a single unit.
  This allows negotiation between factions in order to make up the majority.

 This common behavious is a pretty artificial construct to overcome the
 discussed drawbacks of majoritarian rules.

This occurs in Ireland with our Programme for Government.  After the
election, there is a negotiation between the parties to agree on what
the policies/priorities for the government until the next election
will be.

If the coalition doesn't implement what was agreed, then it could find
that one of its members leaves and the government falls.  This could
lead to a new general election or to a different coalition being
formed.

 A faction can make compromises on issues that it doesn't care about
 in order to get things that it does.  This requires there is no solid
  bloc though.

 And when both factions care about both issues?

Well, they aren't likely to care equally about every issue.  In any
case, negotiations will start for the Every decision decided by
simple majority and negotiations should improve the utility.  It is
possible that total utility would fall as a result of those
negotiations, but that is (hopefully) unlikely.

 Sounds reasonable, the problem is that a) people don't like random methods
 b) it will result in certain outlier elements in society getting some power.

 a) FAWRB is not a random but a very specific and quite sophisticated
 method. It only uses a certain amount of chance, just as many things in
 our life do. Chance should not be mixed up with arbitrariness. Used in a
 rational way, FAWRB will usually elect good compromise options with near
 certainty, not leading to significant amounts of randomness.

I know, but it does have randomness.

Btw, could you create a web page that gives a description of the
method, since it was still in the discussion stage the last time you
posted here.

 Yes, I agree. The version I just proposed to Terry incorporates such a
 threshold.

Great.

 Using majority rule?

Well, majority of the members of Congress.  It may not have passed if
voted directly by the people.

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Re: [EM] Range Voting vs Condorcet (Greg Nisbet)

2008-10-17 Thread Jobst Heitzig

Dear Greg,

you wrote:
Group membership is difficult to define. With ranked ballots it's 
simple, but in the majority criterion debate, I argue that a score of 
60% represents 60% of a first preference, not the preference between 59% 
and 61%. 


Sorry, I don't get your meaning here.

However, it seems to me that there is a confusion about the usage of the 
term majority in the context of our debate. In the majority criterion 
and related criteria, we usually don't speak of *the* majority, 
referring to one specific subset of the electorate, but we refer to *a* 
majority, by which we mean *any* subgroup consisting of more than half 
of the voters.


For example, consider the classical cycle of true preferences, where
  voter X ranks ABC
  voter Y ranks BCA
  voter Z ranks CAB.

In this situation, there are three different majorities: {X,Y}, {Y,Z}, 
and {Z,X}. Of course these groups are not disjoint and it makes no sense 
to speak of the majority. Rather, the majority criterion only requires 
that each of these groups, should they decide to do so, can overrule the 
third voter. That is, X and Y can cooperate in overruling Z and making 
sure B wins. Likewise (but not at the same time of course), Y and Z 
could agree to elect C. So, it usually makes no sense to speak of the 
majority since most often there are lots of majorities - it all depends 
on which of these groups happens to make the deal to overrule the rest.


 ... we have not settled the issue of simultaneous
majorities. 


See above for clarification. There is no issue of simultaneous 
majorities, the criterion simply requires that each subgroup of more 
than half of the voters has a way of overruling the rest. It does not 
require that two such subgroups can do so at the same time, which is 
obviously impossible.


I continued:

While of course civil rights are very important to make sure that
no-one's basic *rights* are violated, they cannot make sure that
everybody's *preferences* are have a fair chance of influencing
decisions that are made *within* the limits the civil rights pose.
 


to which you replied:
Let me explain my point. I set the bar fairly high for tyranny of 
majority i.e. it must constitute actually oppressing me and not merely 
annoying or inconveniencing me to be labelled tyranny. 


I don't care for the label tyranny. My point is that when a majority 
is able to overrule the rest with certainty, then that's not democratic.


You talk about the destruction of 
democracy. 


Did I? I don't think so. I don't think there has been any large-scale 
truly democratic system yet. Only some families and small groups often 
decide in an approximately democratic way when they make sure that each 
member of the group makes a decision at some point in time, for example 
by letting the members decide in turn.


That democracy is an all-or-nothing type thing. I am arguing 
that a good constitution will prevent a majority from acting in such a 
way that democracy itself is subverted. 


Not when the constitution allows the majority to decide all issues 
without having to be concerned about other peoples wishes.


If you argue instead that 
suboptimal results come about, yes I agree with you. 


My point is not the optimality of results, whatever that may mean. To 
define and ensure optimality is a large but different task than to 
ensure the democratic right to influence the decision.


For example, some philosophers argued that it would be optimal if some 
highly intelligent, well-informed and impartial person (the 
philosopher-king) decided all issues. Though I tend to agree that this 
might give optimal results, such a system would obviously be not a bit 
democratic.


On the other hand, simply drawing a random ballot to decide is perfectly 
democratic since it gives each voter exactly the same power regardless 
of factions. However, that method would not give optimal results at 
all since compromise options would get no chance at all. What is missing 
here is an incentive to cooperate.


So, whether a method is democratic and whether it leads to optimal 
results are just two questions which are in large part (but not totally) 
independent. This is why we developed FAWRB, a method which gives each 
voters the same power but gives them also strong incentives to cooperate 
in finding and electing good compromise options.


Again, you speak about actively preventing the majority from doing 
something that violates the rights of minority. Such cannot be prevented 
by any voting method! 


Excuse me! Of course it can. I have demonstrated this over and over. 
With FAWRB, the worst a majority of, say, 55% of the electorate can do 
to the minority is to bullet-vote for the option considered worst to the 
other 45%, thus assigning 55% of the winning probability to that option. 
But this is not violating the minorities rights since at the same time 
those 45% of the voters can assign the remaining 45% of the winning 

Re: [EM] Populism and Voting Theory

2008-10-17 Thread Brian Olson

On Oct 17, 2008, at 9:44 AM, Raph Frank wrote:


Anyway, you would rank PR-STV behind single winner election methods?


As a priority of things to do? Yeah kinda. It's substantially a  
separate issue. There will be single winner elections (mayor,  
governor, president, other one-off seats), and there will be multi- 
member bodies and some of those should be converted to a PR system,  
and for the time being getting better single winner elections could  
apply to all those districted elections. So I think getting ranking/ 
ratings ballots on single winner votes is the single biggest change we  
could make to the electoral system.


But hey, follow your passion. There are plenty of good things to do  
and we should do them all and I think we're most effective when we're  
working on what we personally care most about and in coalition with  
the right allies even if they're focusing on different aspects of the  
movement.



CPO-STV (or maybe Schulze-STV) are obvious improvements, but with big
costs in complexity.  I do think that vote management is a weakness of
PR-STV (I wonder if Schulze STV would stop parties bothering to try).
Also, the district sizes need to be reasonable (say 5+).  In Ireland,
there are 3.86 seats per constituency on average, which I think is to
low.


Oops, I may have written imprecisely. I meant PR-STV to mean the  
general philosophy of having Proportional Representation governing  
bodies, likely elected by a variation on STV.



Also, if you could make one change, would you implement IRNR or
redistricting reform?  Unfortunately, with extreme gerrymandering, I
think most methods would still elect a member of one of the two
parties.


I'm still going for changing single-winner election methods as the  
biggest change, and likely biggest bang-per-buck we can get out of  
changes to work on.


Brian Olson
http://bolson.org/



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Re: [EM] Range Voting vs Condorcet (Greg Nisbet)

2008-10-17 Thread Jobst Heitzig

Dear Raph,

you answered to me:

a) FAWRB is not a random but a very specific and quite sophisticated
method. It only uses a certain amount of chance, just as many things in
our life do. Chance should not be mixed up with arbitrariness. Used in a
rational way, FAWRB will usually elect good compromise options with near
certainty, not leading to significant amounts of randomness.


I know, but it does have randomness.


I includes a chance process just as many sophisticated things in our 
life do. It does not include arbitrariness. It will most often lead to a 
certain winner (one option getting 100% winning probability).


Here's some evidence that the perceptions that chance processes are evil 
and that deterministic processes cannot lead to random results is wrong:


1. Some time ago I challenged you all by asking for a method which 
elects C with certainty in the 55/45-example. The only methods which 
achieved this seeminly simple goal included a chance process.


2. Every majoritarian method leads to a severe kind of randomness when 
there's no Condorcet Winner! This is because in all these situations 
there is no group strategy equilibrium, that is, whatever the winner is, 
there will be some majority having both the incentive and the means to 
change the winner to an option they like better. So, where the strategic 
process will end is mostly random since it cannot settle on an equilibrium.


Yours, Jobst

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Re: [EM] Populism and Voting Theory

2008-10-17 Thread Raph Frank
On Fri, Oct 17, 2008 at 5:03 PM, Brian Olson [EMAIL PROTECTED] wrote:
 But hey, follow your passion. There are plenty of good things to do and we
 should do them all and I think we're most effective when we're working on
 what we personally care most about and in coalition with the right allies
 even if they're focusing on different aspects of the movement.

Well, being Irish, I don't have to do anything, since we already have
PR-STV :).  Though if I was bothered, maybe I would try to have the
constituency sizes increased.

However, that is also sorta happening automatically too.  Gormley is
the Minister for the Enviroment (responsible for setting the election
boundary guidelines) and Green Party (i.e. a small party) leader and
he has modified them so that the constituency commission should aim
for larger constituencies for the council elections.  Some of the
supporters of the larger parties have called it Gormley-mandering
... because more proportionality is clearly evil.  Ofc, they
officially object to the loss of local representation (which moving
from a 3 seater to a 5 seater clearly weakens).

 I'm still going for changing single-winner election methods as the biggest
 change, and likely biggest bang-per-buck we can get out of changes to work
 on.

Hopefully, improved electoral methods would help dull the benfits of
gerrymandering and increase the risks.

The majority party in a two party system have a large incentive to
gerrymander as its members are guaranteed to win the gerrymandered
districts.

Given that voters would have more power to remove legislators with
better voting systems, this is potentially higher risk as it makes
your party look dishonest.

Also, if no party has an outright majority it becomes harder still.

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Re: [EM] Range Voting vs Condorcet (Greg Nisbet)

2008-10-17 Thread Raph Frank
On Fri, Oct 17, 2008 at 5:24 PM, Jobst Heitzig [EMAIL PROTECTED] wrote:
 I know, but it does have randomness.

 I includes a chance process just as many sophisticated things in our life
 do. It does not include arbitrariness. It will most often lead to a certain
 winner (one option getting 100% winning probability).

I am not sure it would in practice.  It is likely that a few percent
would bullet vote.

I think having thresholds at both ends would be a good idea, i.e.
eliminate all options with less than 1/3 support and automatically
elect any option which achieves greater than 75% probability.

 Here's some evidence that the perceptions that chance processes are evil and
 that deterministic processes cannot lead to random results is wrong:

I think it is that random methods have the potential to be easier to
corrupt.  If someone with 5% support wins the draw, there is likely to
be many accusations of it being rigged.

Also, it could have stability problems.

 1. Some time ago I challenged you all by asking for a method which elects C
 with certainty in the 55/45-example. The only methods which achieved this
 seeminly simple goal included a chance process.

I actually do think that it is a reasonable idea, but having it
implemented would be an uphill battle.

I think that a system that results in a 100% winner would be a
reasonable target unless, say more than 1/3 of the voters, refuse to
compromise would be a reasonable target.

Using it for something like a legislature where it is possible to
repeat votes is also potentially a problem, as a losing majority can
'toss the coin' over and over.

 2. Every majoritarian method leads to a severe kind of randomness when
 there's no Condorcet Winner! This is because in all these situations there
 is no group strategy equilibrium, that is, whatever the winner is, there
 will be some majority having both the incentive and the means to change the
 winner to an option they like better. So, where the strategic process will
 end is mostly random since it cannot settle on an equilibrium.

I think it is likely that there would be an honest condorcet winners
in most real cases.  Also, the Smith set should contain candidates
that are at least reasonably similar and anyway, condorcet completion
methods are rarely random.

Btw, again, can you put on the web a full description of the method.
It would be helpful to be able to type FAWRB into google and see the
current version.

You have produced software that implements the method, so you should
include a description of the method it implements.

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Re: [EM] FW: IRV Challenge - Press Announcement

2008-10-17 Thread Kristofer Munsterhjelm

Markus Schulze wrote:

Dear Jonathan Lundell,

I wrote (7 Oct 2008):


Well, the second paper is more general. Here they use
Arrow's Theorem to argue why monotonicity has to be
sacrificed.


You wrote (7 Oct 2008):


Or at least that something has to be sacrificed. Do
you see that as a problem?


Well, monotonicity is actually not needed in Arrow's
Theorem. Therefore, Arrow's Theorem is frequently
stated as saying that no single-winner election
method can satisfy (1) universal admissibility,
(2) Pareto, (3) nondictatorship, and (4) independence
from irrelevant alternatives.

Therefore, using Arrow's Theorem to argue that
monotonicity should be sacrificed to get
compatibility with the other criteria seems
to be odd.


If you want to be generous, you could read the argument as all methods 
fail one of Arrow's criteria; monotonicity failure is a result of this, 
and if a method doesn't fail monotonicity, it'll fail something else. 
That's still odd, though, because you can turn the argument around and 
say well, then if you think Arrow failure makes all methods equal, 
there's no disadvantage to using Condorcet, but if you think some 
criteria are more important than others, then there's an advantage to 
using Condorcet, therefore in any case there's no disadvantage to using 
Condorcet.


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Re: [EM] IRV vs Condorcet vs Range/Score

2008-10-17 Thread Kristofer Munsterhjelm

Dave Ketchum wrote:

I suggest a two-step resolution:
 Agree to a truce between Condorcet and Range, while they dispose of 
IRV as being less capable than Condorcet.

 Then go back to the war between Condorcet and Range.


I think the problem, or at least a part of it, is that if we (the 
election-methods members) were to advocate a method, to be effective, it 
would have to be the same method. Otherwise, we would split the vote, 
as it were, against the status quo. Therefore, both Condorcet and Range 
groups would prefer their own method to win.


If that's true, then one way of uniting without running into that would 
be to show how IRV is bad, rather than how Condorcet or Range is better. 
If there's to be unity (or a truce) in that respect, those examples 
would focus on the properties where both Range and Condorcet, or for 
that matter, most methods, are better than IRV, such as in being 
monotonic, reversal symmetric, etc.


An expected response is that these properties don't matter because they 
happen so rarely. To reply to that, I can think of two strategies. The 
first would be to count failures in simulations close to how voters 
would be expected to act, perhaps with a reasoning of we don't know 
what strategy would be like, but the results would be worse than for 
honesty, so these provide a lower bound. The second would be to point 
to real uses, like Australia's two-party domination with IRV, or Abd's 
argument that TTR states who switched to IRV have results much more 
consistent with Plurality than what used to be the case.


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


Re: [EM] Range Condorcet (No idea who started this argument, sorry; I am Gregory Nisbet)

2008-10-17 Thread Kristofer Munsterhjelm

Jobst Heitzig wrote:

Dear Kristofer,

you wrote:
This is really a question of whether a candidate loved by 49% and 
considered kinda okay by 51% should win when compared to a candidate 
hated by the 49% and considered slightly better than the first by the 
51%. A strict interpretation of the majority criterion says that the 
second candidate should win. The spirit of cardinal methods is that 
the first candidate should win, even though it's possible to make 
cardinal methods that pass strict Majority.


What does this spirit help when the result will still be the 2nd 
instead of the 1st candidate, because the method is majoritarian despite 
all cardinal flavour?


Again looking at my 55/45-example shows clearly that compromise 
candidates are not helped by voters' ability to express cardinal 
preferences but rather by methods which require also majority factions 
to cooperate with minorities in their own best interest, as is the case 
with D2MAC and FAWRB.


Would you bother to answer me on this?


Sorry about that. Because I've been away for some time, I've got a long 
backlog of posts, and I'm working my way through them.


Let's look at your example.

55: A 100  C 80  B 0
45: B 100  C 80  A 0

Range scores are 5500 for A, 4500 for B, and 8000 for C. So C wins. For 
Condorcet, A wins because he's the CW. So Condorcet is strictly 
majoritarian here, while Range is not.


You may say that, okay, the A voters will know this and so strategize:

55: A 100  C 1  B 0
45: B 100  C 80  A 0

In which case A wins. This, I think, is what Greg means when he says 
that a majority can exercise its power if it knows that it is, indeed, 
a majority.


As far as I understand, the methods you refer to aim to make this sort 
of strategy counterproductive.


Because Range isn't majoritarian by default, it doesn't elect A in your 
honest-voters scenario. I would say that from this, it's less 
majoritarian, because majorities don't always know that they are 
majorities. However, it's still more majoritarian than your random 
methods, because in the case that the majority does coordinate, it can 
push through its wishes.


To answer your question: the spirit helps because majorities are not 
always of one block, or the same. You have shown that it's possible to 
be less majoritarian than Range, though.


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[EM] Voting Theory and Populism

2008-10-17 Thread Greg Nisbet
So yeah... let's assume you have some amount of political capital to get
this done. You cannot impose loads of reforms at once on people; it doesn't
work. If you had to choose only among the options that you think you could
get done, which would it be?

I support TRS. Minimal minimal effort and better for the people than
primaries!


Message: 5
Date: Fri, 17 Oct 2008 09:09:16 -0400
From: Brian Olson [EMAIL PROTECTED]
Subject: Re: [EM] Populism and Voting Theory
To: Election Methods Mailing List [EMAIL PROTECTED]
Cc: Greg Nisbet [EMAIL PROTECTED]
Message-ID: [EMAIL PROTECTED]
Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes

On Oct 16, 2008, at 10:11 PM, Greg Nisbet wrote:

 Which system do you think would work best that is actually achievable?

That's like asking the oft asked question, 'which candidate is
electable?' and I HATE that question.
It's like suggesting that we prematurely compromise and compress our
election reform advocacy down to a single method to push for when I'd
much rather say that I support: 1. IRNR, 2. Condorcet, 3. IRV, 4.
Approval. And sometimes I want a side of PR-STV, redistricting and
elimination of bad voting machines.

 = Uhh, sorry? I'm not trying to say that IRNR, some unspecified version of
Condorcet, IRV, or approval will never happen. I'm just asking you to weigh
the likelihood of public acceptance in addition to the merit of the method
itself. I am not proposing we end the discussion of which voting method is
best, far from it. I merely want to know which would be the best investment.

=If you object to this question this strongly, please don't respond to it.

In my few years of election reform advocacy, nearly everyone I've
talked to agrees that 'rankings ballots' or 'ranked choice voting' is
a good idea. Probably 80-90% of people I talk to I've been able to
convince that IRV is severely suboptimal (but better than nothing) and
that Condorcet methods are better. Maybe I should try to write down
the elevator pitches/stump speechs/good lines/patter that seem to work
and put together a pamphlet for election reform advocates.

=Go right ahead. In my, uh, few days of talking about this, I've noticed
that some voting methods have definitely fallen out of favor (IRV, Borda,
vanilla Bucklin…) as serious propositions among knowledgeable people.

= I would love a reference of the greatest voting rants of all time.

Message: 6
Date: Fri, 17 Oct 2008 14:44:43 +0100
From: Raph Frank [EMAIL PROTECTED]
Subject: Re: [EM] Populism and Voting Theory
To: Brian Olson [EMAIL PROTECTED]
Cc: Greg Nisbet [EMAIL PROTECTED], Election Methods Mailing
   List [EMAIL PROTECTED]
Message-ID:
   [EMAIL PROTECTED]
Content-Type: text/plain; charset=ISO-8859-1

On Fri, Oct 17, 2008 at 2:09 PM, Brian Olson [EMAIL PROTECTED] wrote:
 That's like asking the oft asked question, 'which candidate is electable?'
 and I HATE that question.
 It's like suggesting that we prematurely compromise and compress our
 election reform advocacy down to a single method to push for when I'd much
 rather say that I support: 1. IRNR, 2. Condorcet, 3. IRV, 4. Approval. And
 sometimes I want a side of PR-STV, redistricting and elimination of bad
 voting machines.

That is a good point, for a group that all accepts plurality is bad,
it is still in effect used for polling purposes.

I would probably go

1: Approval (slightly ahead of condorcet)
1: Condorcet
2: IRNR
3. IRV

= Where would Range fit in, just out of curiosity? Of the things that are
listed, I completely agree with this.

I don't think IRNR is sufficiently examined to really know where to
put it though.  It might have serious strategy issues.

= I'd be skeptical of any iterative method. IRV, STV, Raynaud, Nanson,
Baldwin etc. all have flaws with them. Any method that relies on rejecting
candidates and recursively applying itself will run into problems. IRNR is
light years ahead of other iterative methods though.

Anyway, you would rank PR-STV behind single winner election methods?

I would rate PR-STV as one of, if not the best voting system (and
certainly one of the best system that is actually in use).  It also
has the added advantage that it is also a redistricting reform (or at
least makes redistricting less important).

CPO-STV (or maybe Schulze-STV) are obvious improvements, but with big
costs in complexity.  I do think that vote management is a weakness of
PR-STV (I wonder if Schulze STV would stop parties bothering to try).
Also, the district sizes need to be reasonable (say 5+).  In Ireland,
there are 3.86 seats per constituency on average, which I think is to
low.

=Why have constituencies at all?

Also, if you could make one change, would you implement IRNR or
redistricting reform?  Unfortunately, with extreme gerrymandering, I
think most methods would still elect a member of one of the two
parties.

= Now you're getting it, you have to compromise with non-voting-theorists
here. I'd say go for the voting method. That will break 

[EM] Making a Bad Thing Worse

2008-10-17 Thread Greg Nisbet
The United States uses FPTP, surprise surprise. However how bad would FPTP
really be if you remove some of the stupidity?

1) Primaries

Especially the presidential primaries. Why Iowa and New Hampshire I ask you?
The Republican winner-takes-state primaries are especially bad. The will of
the people is distorted. And the winners of primaries get legal protection.

2) Sore loser laws

If you lose a primary, you can't even run in some areas. The state will
attempt to prevent you from stealing votes away from your party.

3) Really bad ballot access laws.

If people can't even run... it doesn't matter what voting method you are
using.

4) The Electoral College

Someone explain to me how this makes sense. We elect a group of 538 people
who will then elect one person. Umm... why elect these people? They aren't
doing anything complicated, they are just signing their name and the name of
a candidate. Electing Congress makes sense, how else would you handle the
loads of legislation that they create every so often?

5) The Senate

States aren't represented by their population. This means rural bias etc.
How can their opinion be regarded as representing America's?

6) The House

Whose bright idea was it to let the states decide how to redistrict
themselves? Seriously.

7) Gerrymandering

In addition to (6) and gerrymandering at the local level, the state
boundaries themselves were gerrymandered. It was mostly due to slavery, but
the vestiges of these funky decisions still remain. There are also a ton of
low-population states between California and the Mississippi River, whose
brilliant idea was that?

8) Two Parties

This might be a consequence of FPTP, but seriously. The Libertarian Party,
the third largest, is still TINY by comparison to the Democrats and
Republicans. It is no wonder we have so many independents in this country.
Many people dislike both parties but have no idea what to do. The UK and
Canada seem to manage more parties.

9) Elections on Tuesday

why not make election day a holiday? or hold it on weekends?

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Re: [EM] Making a Bad Thing Worse

2008-10-17 Thread Raph Frank
On Sat, Oct 18, 2008 at 1:41 AM, Greg Nisbet [EMAIL PROTECTED] wrote:
 The United States uses FPTP, surprise surprise. However how bad would FPTP
 really be if you remove some of the stupidity?

 1) Primaries

 Especially the presidential primaries. Why Iowa and New Hampshire I ask you?
 The Republican winner-takes-state primaries are especially bad. The will of
 the people is distorted. And the winners of primaries get legal protection.

This shouldn't be an issue at all.  Parties should be allowed to pick
whoever they want, however they want.

I think, if you are going to have plurality, then it's probably better
to have them than not.

 2) Sore loser laws

 If you lose a primary, you can't even run in some areas. The state will
 attempt to prevent you from stealing votes away from your party.

Yeah, that is bad, candidates should be allowed to run if they want.

 3) Really bad ballot access laws.

 If people can't even run... it doesn't matter what voting method you are
 using.

Agreed.  Apparently, a federal law that allowed anyone with 2000
signature automatic ballot access to any given race would be unlikely
to result in more than 10 or so on any given ballot.  Would anyone
bother to collect 100k signatures in order to put 50 names on the
ballot?

Also, there are some criminal laws linked to this, so collecting
signatures could put you at risk.

 4) The Electoral College

 Someone explain to me how this makes sense. We elect a group of 538 people
 who will then elect one person. Umm... why elect these people? They aren't
 doing anything complicated, they are just signing their name and the name of
 a candidate. Electing Congress makes sense, how else would you handle the
 loads of legislation that they create every so often?

It is a good idea.  But it seems like it was broken from the start.
The Electoral College should meet and then make its decision.

This is compounded by the fact that all states have switched to winner
takes all methods of selecting the electors, so it is double broken.

 5) The Senate

 States aren't represented by their population. This means rural bias etc.
 How can their opinion be regarded as representing America's?

Well, in theory, the US is a federation, not a democracy.  In any
case, that requires 100% of the States to agree for it to be changed.

OTOH, if you want to be evil, you could strip the Senate of all its
power, that would 'only' require 75% of the States.

 6) The House

 Whose bright idea was it to let the states decide how to redistrict
 themselves? Seriously.

The same people who let legislatures redistrict for themselves.

In fact, I think that having the States do the redistricting is better
than allowing Congress do it.  If the States were independently
controlled, then there is less of a conflict of interest.

However, the 2 party system is entrenched, so the State legislatures
aren't independent.

 7) Gerrymandering

 In addition to (6) and gerrymandering at the local level, the state
 boundaries themselves were gerrymandered. It was mostly due to slavery, but
 the vestiges of these funky decisions still remain. There are also a ton of
 low-population states between California and the Mississippi River, whose
 brilliant idea was that?

I think that once off gerrymandering isn't as bad as gerrymandering
after the census.

It isn't self reinforcing.  As time passes, things change.  With
Congressional boundaries, they are re-adjusted as things change to
cancel it out.  You can't readjust State boundaries.

 8) Two Parties

 This might be a consequence of FPTP, but seriously. The Libertarian Party,
 the third largest, is still TINY by comparison to the Democrats and
 Republicans. It is no wonder we have so many independents in this country.
 Many people dislike both parties but have no idea what to do. The UK and
 Canada seem to manage more parties.

There is a need for 3rd parties to concentrate their efforts on
specific areas.  The problem is that the 2 parties use their power to
reinforce the 2 party system.

Also, each level of government is held by the 2 parties, so it is hard
to break it.

Anyway, maybe the Libertarians should pick a state and focus all their
national effort on getting a Libertarian elected to the House of
Representatives in that State.  Once they achieve that, they can move
on to getting a second one elected from the State.  Ofc, their seat
would likely be gerrymandered away since their Representative wouldn't
be a member of one of the two parties.

Maybe the reason that 3rd parties are more viable in the UK and Canada
is that there is more independence in setting the boundaries.  This
means that they can't be gerrymandered out of existence if they manage
to get one seat.

 9) Elections on Tuesday

 why not make election day a holiday? or hold it on weekends?

I thought they were held over multiple days with 'early voting', or
was that changed?

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Re: [EM] Making a Bad Thing Worse

2008-10-17 Thread Greg Nisbet
On Fri, Oct 17, 2008 at 6:17 PM, Raph Frank [EMAIL PROTECTED] wrote:

 On Sat, Oct 18, 2008 at 1:41 AM, Greg Nisbet [EMAIL PROTECTED]
 wrote:
  The United States uses FPTP, surprise surprise. However how bad would
 FPTP
  really be if you remove some of the stupidity?
 
  1) Primaries
 
  Especially the presidential primaries. Why Iowa and New Hampshire I ask
 you?
  The Republican winner-takes-state primaries are especially bad. The will
 of
  the people is distorted. And the winners of primaries get legal
 protection.

 This shouldn't be an issue at all.  Parties should be allowed to pick
 whoever they want, however they want.

 I think, if you are going to have plurality, then it's probably better
 to have them than not.


Thanks for bringing this up, it is a perfectly valid criticism. I don't
disagree with this point, but it technically isn't in conflict with what I
said. First of all I argue two things, I didn't state them initially.

1) Primaries are anti-utilitarian.
2) The Government enforcing any way for parties to operate is bad.

It's sort of catch-22 I know. But think of it this way, we allow people to
conduct elections based on FPTP. None of us advocated banning private FPTP
elections. However, that does not stop us from criticizing their choice of
method.

The second point I don't agee with because Median Voter would suggest that
candidates would be more centrist on average if primaries didn't exist. I
like moderates better than Democrats or Republicans and I think they are
better for the country...



  2) Sore loser laws
 
  If you lose a primary, you can't even run in some areas. The state will
  attempt to prevent you from stealing votes away from your party.

 Yeah, that is bad, candidates should be allowed to run if they want.


If you let anyone who wants to be on the ballot be on the ballot, how bad
would that really be?



  3) Really bad ballot access laws.
 
  If people can't even run... it doesn't matter what voting method you are
  using.

 Agreed.  Apparently, a federal law that allowed anyone with 2000
 signature automatic ballot access to any given race would be unlikely
 to result in more than 10 or so on any given ballot.  Would anyone
 bother to collect 100k signatures in order to put 50 names on the
 ballot?


I think an average voter would not get confused by large numbers of
candidates. If they were organizes reasonably, the voter strictly benefits
because they could always voter against unknown candidates as a matter of
principle. Most do, so I don't see what people are whining about.


 Also, there are some criminal laws linked to this, so collecting
 signatures could put you at risk.

  4) The Electoral College
 
  Someone explain to me how this makes sense. We elect a group of 538
 people
  who will then elect one person. Umm... why elect these people? They
 aren't
  doing anything complicated, they are just signing their name and the name
 of
  a candidate. Electing Congress makes sense, how else would you handle the
  loads of legislation that they create every so often?

 It is a good idea.  But it seems like it was broken from the start.
 The Electoral College should meet and then make its decision.



I have to disagree with you on that one. I do not see it doing anything
useful. It either corrects the people's will (in which case it is
paternalistic and evil) or it does nothing making it a giant waste of
resources.



 This is compounded by the fact that all states have switched to winner
 takes all methods of selecting the electors, so it is double broken.

  5) The Senate
 
  States aren't represented by their population. This means rural bias etc.
  How can their opinion be regarded as representing America's?

 Well, in theory, the US is a federation, not a democracy.  In any
 case, that requires 100% of the States to agree for it to be changed.


Umm federation and democracy are not mutually exclusive. Anyway, my opinion
might be biased because I live in California, the state most screwed over by
the system. I do not buy the whole prevent tyrannical regions from taking
over nonsense b/c preventing tyranny is a civil rights issue not a voting
system issue. Attempting to design some system to subvert the will of the
voters for their own good is not to be trusted.


 OTOH, if you want to be evil, you could strip the Senate of all its
 power, that would 'only' require 75% of the States.


 6) The House

 Whose bright idea was it to let the states decide how to redistrict
 themselves? Seriously.

The same people who let legislatures redistrict for themselves.

 In fact, I think that having the States do the redistricting is better
 than allowing Congress do it.  If the States were independently
 controlled, then there is less of a conflict of interest.


Not exactly. You just have mini conflicts of interest that don't all line up
in one direction instead of one big one.




 However, the 2 party system is entrenched, so the State legislatures
 aren't 

Re: [EM] Making a Bad Thing Worse

2008-10-17 Thread Jonathan Lundell

On Oct 17, 2008, at 6:56 PM, Greg Nisbet wrote:

I think you need to prove you have some 'valid reason' to vote  
early. Anyway, I know there are some restrictions that make it  
inconvenient otherwise who would show up at the polls?


Depends on the state. In California, you just have to ask, and many  
county registrars encourage you to ask. You can ask for a single  
election, or become a permanent absentee voter.


Oregon is exclusively vote-by-mail, as is my precinct in California.

Since mail-in ballots must be received by election day (postmarks  
don't count), it's inherently an early-voting system. In California,  
ballots are mailed out about 30 days before the election, which makes  
life difficult for candidates. Oregon says 14-18 days, which seems  
more than adequate.


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Re: [EM] Making a Bad Thing Worse

2008-10-17 Thread Kathy Dopp
 Date: Sat, 18 Oct 2008 02:17:14 +0100
 From: Raph Frank [EMAIL PROTECTED]
 Subject: Re: [EM] Making a Bad Thing Worse
 The Electoral College should meet and then make its decision.

 This is compounded by the fact that all states have switched to winner
 takes all methods of selecting the electors, so it is double broken.


That is not quite true. There are two states, Maine and one other (I
forget which) that proportionally split their electoral votes.
Recently there was an effort by Republicans to have CA split its
electoral votes proportionally - but Dems fought it because it would
have virtually guaranteed that Republicans win the Presidential
contest.

Kathy

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Re: [EM] Making a Bad Thing Worse

2008-10-17 Thread Jonathan Lundell

On Oct 17, 2008, at 7:11 PM, Kathy Dopp wrote:


Date: Sat, 18 Oct 2008 02:17:14 +0100

From: Raph Frank [EMAIL PROTECTED]
Subject: Re: [EM] Making a Bad Thing Worse
The Electoral College should meet and then make its decision.

This is compounded by the fact that all states have switched to  
winner

takes all methods of selecting the electors, so it is double broken.



That is not quite true. There are two states, Maine and one other (I
forget which) that proportionally split their electoral votes.
Recently there was an effort by Republicans to have CA split its
electoral votes proportionally - but Dems fought it because it would
have virtually guaranteed that Republicans win the Presidential
contest.


That is not quite true. Maine and Nebraska assign their electoral  
votes by the winner in each congressional district, and the two extra  
votes by the statewide vote. In practice, neither state has ever split  
their electoral vote (though Obama may have a shot at the district  
containing Omaha this year).


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Re: [EM] IRV vs Condorcet vs Range/Score

2008-10-17 Thread Dave Ketchum

On Fri, 17 Oct 2008 22:08:32 +0200 Kristofer Munsterhjelm wrote:

Dave Ketchum wrote:


I suggest a two-step resolution:
 Agree to a truce between Condorcet and Range, while they dispose 
of IRV as being less capable than Condorcet.

 Then go back to the war between Condorcet and Range.



I think the problem, or at least a part of it, is that if we (the 
election-methods members) were to advocate a method, to be effective, it 
would have to be the same method. Otherwise, we would split the vote, 
as it were, against the status quo. Therefore, both Condorcet and Range 
groups would prefer their own method to win.


If that's true, then one way of uniting without running into that would 
be to show how IRV is bad, rather than how Condorcet or Range is better. 
If there's to be unity (or a truce) in that respect, those examples 
would focus on the properties where both Range and Condorcet, or for 
that matter, most methods, are better than IRV, such as in being 
monotonic, reversal symmetric, etc.


First, IRV will slay us all if we do not attend to it - it is getting USED.

Range and Condorcet are among the leaders and ask two different conflicting 
thought processes and expressions of the voters:
 Condorcet ranks per better vs worse, but asks not for detailed 
thought:  ABC ranks A as best of these three.
 Range easily rates A-100 and C-0.  Same thought as for Condorcet 
would rate B between them, but deciding exactly where can be a headache.
 Each of these has its backers, but we cannot devote full time to this 
battle while we need to defend our turf against IRV.


I suggest concentrating on Condorcet disposing of IRV because both use 
almost identical rank ballots and usually agree as to winner.  They look at 
different aspects:
 Condorcet looks only at comparative ranking.  When they matter, we 
ask only whether AB or BA is voted by more voters.
 IRV cares only what candidate ranks first on a ballot, though it 
looks at next remaining candidate after discarding first ranked as a loser.

 Sample partial election:
9 AE
9 BA
   18 CA
   20 DA
 A is WELL LIKED HERE and would win in Condorcet.  Count one last 
voter for IRV:

 A - B and C lose, and D loses to A.
 B - A, E, and B lose, and C loses to D.
 C or D - D wins.

What Condorcet calls cycles inspire much debate.  Optimum handling does 
deserve thought, but could be directed more as to how to resolve them. 
Real topic is that comparing rankings can show three or more of the best 
candidates are close enough to ties to require extra analysis.
 I claim this is a comparatively good thing - the worst candidates end 
up outside the cycles and it is, at least, no worse than random choice to 
award the win to what is seen as the best of them.


Having election results in understandable format is valuable for many purposes:
 Condorcet records all that it cares about for any district, such as 
precinct, in an N*N array.  These arrays can be summed for larger districts 
such as county or state.  Also they can be published, in hopefully 
understandable form, for all interested.

 Range has less information to make available.
 IRV talks of recounting ballots as it steps thru discarding losers - 
at any rate not as convenient as Condorcet.


An expected response is that these properties don't matter because they 
happen so rarely. To reply to that, I can think of two strategies. The 
first would be to count failures in simulations close to how voters 
would be expected to act, perhaps with a reasoning of we don't know 
what strategy would be like, but the results would be worse than for 
honesty, so these provide a lower bound. The second would be to point 
to real uses, like Australia's two-party domination with IRV, or Abd's 
argument that TTR states who switched to IRV have results much more 
consistent with Plurality than what used to be the case.


Condorcet has no interest in being like Plurality.  Its big plus over 
Plurality is letting voters rank those candidates they want to rank as 
best, etc., and using this data.


Simulations are tricky - when can we honestly claim expected matches reality?
--
 [EMAIL PROTECTED]people.clarityconnect.com/webpages3/davek
 Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
   Do to no one what you would not want done to you.
 If you want peace, work for justice.




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