comments" thread, Mike Ossipoff wrote (Fri. Jan7):
CB: Don't you read Marcus Schulze's posts? He is one of the more erudite and intelligent members of this list.You continued: If a method (like RV) that fails May's criterion/axiomI reply: I don't know what May's criterion or axiom is, but I can predict that it probably won't be as important to me as the criteria that measure what a majority has to do in order to make someone lose. That's because I want to get rid of the lesser-of-2-evils problem, in which voters must abandon their favorite in order to make a greater-evil lose.
He wrote (Sat.Jan.1):
Hallo, Chris Benham wrote (1 Jan 2005): > To me, it is axiomatic that a single-winner voting method > should, with sincere voting, reduce to FPP when there are > only two candidates. Mike Ossipoff replied (1 Jan 2005): > Axiomatic? You're giving to us a fundamental standard that > you have. That's your axiom. You mustn't expect everyone > to have the same axioms that you have. That's not Benham's criterion. That's May's criterion: If there are only two candidates A and B and the number of voters who strictly prefer candidate A to candidate B is strictly larger than the number of voters who strictly prefer candidate B to candidate A, then candidate A must be elected with certainty. Markus Schulze Marcus again (Mon.Jan.3): Dear Craig, you wrote (3 Jan 2005): > Here is a brief description of the 1952 May 'theorem' I got from the > Internet: > > | May's theorem: When choosing among only two options, there is only one > | social decision rule that satisfies the requirements of anonymity, > | neutrality , decisiveness and positive responsiveness, and it is the > | majority rule. May also presumed that the result depends only on whether the individual voter strictly prefers candidate A to candidate B, strictly prefers candidate B to candidate A or is indifferent between candidate A and candidate B, but it must not depend on the ratings of the individual voters for the different candidates (Kenneth O. May, "A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decision," Econometrica, vol. 20, pp. 680--684, 1952). However, Hylland proved that when there are only two candidates and the used single-winner election method is strategyproof then the result depends only on whether the individual voter strictly prefers candidate A to candidate B, strictly prefers candidate B to candidate A or is indifferent between candidate A and candidate B (Aanund Hylland, "Strategy Proofness of Voting Procedures with Lotteries as Outcomes and Infinite Sets of Strategies," University of Oslo, 1980). Therefore, I interpret May's theorem in connection with Hylland's theorem as follows: When there are only two candidates then the unique anonymous, neutral, decisive, and strategyproof single-winner election method is FPP. Therefore, every single-winner election method should satisfy the following criterion: When there are only two candidates and the number of voters who strictly prefer candidate A to candidate B is strictly larger than the number of voters who strictly prefer candidate B to candidate A, then candidate A should be elected with certainty. Markus Schulze CB: I'm having trouble trying to paste some more quotes, so I post this and continue in another message. Chris Benham
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