[EM] Fwd: 3 or more choices - Condorcet

[Juho Laatu]

Resent. Also I seem to have some problems getting my mails through on the list.

Juho


Begin forwarded message:

> From: Juho Laatu
> Date: 8. 11 2012 20.32.01 UTC+2.00
> To: EM list
> Subject: Re: [EM] 3 or more choices - Condorcet
> 
> On 8.11.2012, at 18.55, Chris Benham wrote:
> 
>> Robert Bristow-Johnson wrote (1 Oct 2012):
>> 
>> "my spin is similar.  Ranked Pairs simply says that some "elections" (or 
>> "runoffs") speak more loudly than others.  those with higher margins are 
>> more definitive in expressing the will of the electorate than elections 
>> with small margins.  of course, a margin of zero is a tie and this says 
>> *nothing* regarding the will of the electorate, since it can go either way.
>> 
>> the reason i like margins over winning votes is that the margin, in vote 
>> count, is the product of the margin as a percent (that would be a 
>> measure of the decisiveness of the electorate) times the total number of 
>> votes (which is a measure of how important the election is).  so the 
>> margin in votes is the product of salience of the race times how 
>> decisive the decision is."
> 
>> Say there are 3 candidates and the voters have the option to fully rank them,
>> but instead they all just choose to vote FPP-style thus:
>> 
>>  
>> 49: A
>> 48: B
>> 03: C
>>  
>> Of course the only possible winner is A. Now say the election is held again (with
>> the same voters and candidates), and the B voters change to B>C giving:
>> 
>> 49: A
>> 48: B>C
>> 03: C
>> 
>> Now to my mind this change adds strength to no candidate other than C, so the winner 
>> should either stay the same or change to C. Does anyone disagree?
> 
> The change of 48 vote fragments from "C=A" to "C>A" adds strength to C and adds weakness to A. Condorcet methods often concentrate on the strength of losses to other candidates.
> 
>>  
>> So how do you (Robert or whoever the cap fits) justify to the A voters (and any fair-minded
>> person not infatuated with the Margins pairwise algorithm) that the new Margins winner is B??
> 
> Candidate A now loses to one candidate in a pairwise comparison instead of winning all others, so A might not win this time.
> 
>>  
>> The pairwise comparisons: B>C 48-3,  C>A 51-49,  A>B 49-48.
>> Ranked Pairs(Margins) gives the order B>C>A. 
>> 
>> I am happy with either A or C winning, but a win for C might look odd to people accustomed
>> to FPP and/or IRV.
>>  
>> *If* we insist on a Condorcet method that  uses only information contained in the pairwise
>> matrix (and so ignoring all positional or "approval" information) then *maybe* "Losing Votes"
>> is the best way to weigh the pairwise results. (So the strongest pairwise results are those where
>> the loser has the fewest votes and, put the other way, the weakest results are those where the
>> loser gets the most votes).
> 
> With sincre votes the implications of the result in real life after the election (strongest defeat / strength of opposition against the winner in this case) is one good approach to determining which method is the most sensible one. In the example all candidates lose to one other candidate (= the candidate that is the strongest opponent in opposition).
> 
> - Margins measure the strength of opposition as "how many more supporters does the opposition have (when compared to the number of supporters of the winner)"
> 
> - Proportions measure the strength of opposition as "how many times more supporters does the opposition have (when compared to the number of supporters of the winner)"
> 
> - Losing Votes measure the strength of opposition as "how many people would defend the winner (assuming that opposition has more supporters, but not putting any weight on how many)"
> 
> - Winning Votes measure the strength of opposition as "how many people would oppose the winner (assuming that oppostion has more supporters, but not putting any weight on how many defenders there are)"
> 
> All these make at least some sense in real life. But losing and winning votes are somewhat limited in the sense that the number of (respectively) winning or losing votes has no impact on the strength/weakness of the winner.
> 
> My first concern with the nature of sincere margins as a way to measure the quality of the winner as "ability to defend against oppostion" is if proportions make more sense than margins or not. Margins are simpler. Proportions say that 49-48 defeat is weaker than 48-47 defeat.
> 
> (One additional interesting question is what all the ties mean. If we use the pairwise matrix only and assume sincerity, maybe the default interpretation is that all the ties are intentional (not e.g. a result of voters being too tired to mark all their sincere opinions in the ballot).)
> 
> Juho
> 
> 
>>  
>> In the example Losing Votes elects A. Winning Votes elects C which I'm fine with, but I don't
>> like Winning Votes for other reasons.
>> 
>> Chris Benham
>>  
>>  
>>  
>> ----
>> Election-Methods mailing list - see http://electorama.com/em for list info
> 

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