I worked up some examples. I doubted that three-slot MMPO would still permit Majority failures, so I tried to make one. This is the closest I could come:
10 A>BC>D 10 B>CA>D 10 C>AB>D 10 DA>B>C 10 DB>C>A 10 DC>A>B Half the voters prefer {A,B,C} to D, and MMPO shows a four-way tie among all candidates. To create a failure, we need one more voter to prefer ABC to D, but we need D's MMPO score to drop relative to the others'. I don't think this is possible. Now for some Condorcet failures: 30 B>C 19 AB 51 AC CW is C, but MMPO winner is A. 5 B>C 10 C>A 85 AB CW is A, but MMPO winner is B. And I was dismayed to find that it isn't enough to disallow equal ranking: 29 B 19 A>B 9 A>C 43 C CW is C, but the MMPO winner is A. This scenario is particularly interesting because A is either a "weak centrist" candidate, or else someone taking advantage of the Later-no-help failure. This might be pretty bad. Suppose the following results are predicted: 49 Bush 24 Gore 27 Martian candidate All the Martian supporters need to do is vote "Martian>Gore" to ensure a Martian-Gore tie. The only way this can be countered is by Bush and/or Gore voters having the strategic sense to vote "Bush>Gore" or "Gore>Bush" (keeping in mind that MMPO satisfies Later-no-harm, and so can't make their favorite lose). Interesting, I think. Kevin Venzke Découvrez le nouveau Yahoo! Mail : 250 Mo d'espace de stockage pour vos mails ! Créez votre Yahoo! Mail sur http://fr.mail.yahoo.com/ ---- Election-methods mailing list - see http://electorama.com/em for list info