James, Here is an example of yours that we've been discussing. Preferences 26: A>>C>B 22: A>>B>C 19: C>B>>A 06: C>>B>A 22: B>C>>A 05: B>>A>C
Direction of defeats A>C 52-48 C>B 51-49 B>A 52-48 Approvals: A48, B46, C47. A is the only candidate that is not pairwise beaten by a more approved candidate, so the Approval Plurality criterion says only A can win. DMC and AM meet that criterion, while AWP elects B. While I think that for the "real world" any case for violating AP (especially in favour of the least approved candidate) is too subtle and sophisticated, suppose for the sake of argument that I agree to demote AP from "essential" to merely "highly desirable". One of your arguments against DMC and AM in this example has been that if B is elected, the complaint of the C supporters is undermined by the fact that they won't want to insist on the AP criterion being met because that would result in the election of the candidate they all rank last. Here at least is a method that elects C, that I'll label "Approval Regret". "Voters rank the candidates and insert an approval cutoff. Elect the CW if there is one. If not, compute the "approval regret" score of each Smith-set member thus: consider each in turn as the provisional winner and count how many ballots that don't approve this candidate could have made a candidate they do approve the CW by Compromising. Elect the candidate with the lowest such score. Break a tie by electing the tied candidate with the larger approval score." Taking the example above, there is no CW and all the candidates are in the Smith set. A's approval regret score is 19 because the the 19 C>B>>A voters could have made B the CW by voting B>C>>A. The scores for B and C are 0. C is more approved and so wins. (Without this tiebreaking provision, "Approval Regret" could be a criterion that AWP maybe meets.) So what do you think of this mad idea? Of course its big problem is the complaint of those who prefer A to C (more than half the voters) who can demand that the method meets the AP criterion. Denying such a "motherhood" criterion is just too messy. Chris Benham Find local movie times and trailers on Yahoo! Movies. http://au.movies.yahoo.com ---- Election-methods mailing list - see http://electorama.com/em for list info