Dear Nicholas, you wrote (13 June 2012):
> Actually, on a weird second thought, wouldn't a method that refused to > identify a winner in a three-way tie (Condorcet paradox) be compatible > with both? In Woodall's terminology, the output of an election method is a probability distribution on the set of candidates. He defines the participation criterion as follows: Suppose a set of voters is added where each voter strictly prefers every candidate of set _A_ to every other candidate. Then the probability that the winner is chosen from set _A_ must not decrease. In my paper (http://m-schulze.webhop.net/schulze1.pdf), the output of an election method is a set of winners _W_ rather than a single winner. In (4.7.16) -- (4.7.17), I define the participation criterion as follows: Suppose a set of voters is added where each voter strictly prefers every candidate of set _A_ to every other candidate. Suppose the intersection of _A_ and _W_ was non-empty, then the intersection of _A_ and _W_ must be non-empty afterwards. Suppose _W_ was a subset of _A_, then _W_ must be a subset of _A_ afterwards. It is easy to see that Moulin's proof also works when Woodall's or my definition of the participation criterion is used. Markus Schulze ---- Election-Methods mailing list - see http://electorama.com/em for list info
