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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