Dear Mike, you wrote (4 March 2003): > MMC says: > > If there is a set of candidates such that a majority of the voters > strictly prefers each candidate of this set to each candidate > outside this set, then the winner must be a candidate of this set. > > If that were MMC, then no method would meet MMC. Saying that a > majority prefer the candidates in set S to all the other candidates, > but not saying anything about how they vote, no one can guarantee who > will win then. > > Either you should speak of a majority _voting_ the candidates in S > over all the other candidates, or else, when saying only that they > prefer the candidates in S to all the others, you should add the > stipulation that they vote sincerely.
We've talked about this before in connection with a paper by Pattanaik and Peleg ("P&P"). I agree to Blake Cretney's way of seeing this. Blake wrote to Mike (28 Jan 2002): > Having said all that, I'll get to how I interpret P&P. P&P talk about > ballots, and criteria and methods based on those ballots. By ballots I > could just as easily say preference orders. I don't think P&P intend to > propose a theory in which the preference orders are mental states, but > the method works on actual ballots, so the ballots must be "sincere", > whatever that might mean. They ignore the sincerity issue. They just > have methods and criteria that refer to preference orders. But where > those preference orders come from isn't their concern. For you, > preference order implies sincere preferences, and you recognize that a > real-world method can only work on cast votes. But for P&P, a method is > just a function from a hypothetical set of preference orders to a set of > winners. I absolutely agree with Blake: "A method is just a function from a hypothetical set of preference orders to a set of winners. Where the preference orders come from is of no concern." Markus Schulze ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em