As Kevin pointed out in one of his posts I have been using a overly difficult standard of Favorite Betrayal.
Here's a simpler proof based on the following definition of FBC: Raising favorite to top rank must not decrease expected utility. Given three voters with utilities consistent with the ranked preferences 1 A>B>>C 1 B>>C>A 1 C>>A>B Sincere pure ordinal ballots would be 1 A>B>C 1 B>C>A 1 C>A>B Neutrality and anonimity require that A, B, and C win with equal probability, so the expected utility for the A voter is below the utility of B. Swapping B and A on that ballot yields 1 B>A>C 1 B>C>A 1 C>A>B Clone immunity together with Majority Rule in the two candidate case implies that B wins with this ballot set. Moving favorite back up to top rank displaces B down a rank because we are still assuming pure rankings. This puts us back where we started with less utility than B. That's it. ---- election-methods mailing list - see http://electorama.com/em for list info
