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