2007/12/31, Kevin Venzke <[EMAIL PROTECTED]>: > > Hi Diego, > > --- Diego Santos <[EMAIL PROTECTED]> a écrit: > > Definition: "Some candidate X is a potential winner if, for all Y that > > beats > > X, the margin of Y against X is lesser than the greatest margin of > > another > > candidate against Y". The winner is the Condorcet winner among potential > > winners". > > > > This method meets mono-add-top and I think also Smith, because always > > Minimax(margins) and Smith//Minimax(margins) winners are potential, > > although > > Markus said that no known method passes both criteria > > Am I correct that in the following scenario: > > 49 A > 24 B > 27 C>B > > Your method selects A and B as "potential winners" and elects B?
Yes, you are right. Specifically: A's loss to B is weaker than B's loss to C. B's loss to C is > weaker than C's loss to A. Only C's loss to A is stronger than A's loss to > B. Then, the CW between A and B is B. B is not a potential winner of > either > Minmax(margins) or Smith//Minmax(margins). I not said the "final" winner of my method is the same of Minimax(margins) or Smith//Minimax(margins), but that s/he is in "potetial winner set" (Santos Set?), in this case, A. Mono-add-top is a very difficult criterion to satisfy if the method only > regards pairwise contests. When you add an A>B>C>D ballot there is no > record in the matrix that the top preference on this ballot was A. You > need > a way to ensure that if A wins, A remains the winner no matter what other > information is on the new ballot. I can barely think how to do this, let > alone how to do it when Smith compliance is also needed. > > Kevin Venzke > In your example, I don't see any way that B > A > C, B > C > A or B > A = C ballots can cause other candidate different from B to be CW. ________________________________ Diego Santos
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