My recent "MinMax" message concluded with a half-hearted attempt at a system combining Approval and Condorcet. I have a much better proposal now, although I'm not entirely certain of its merits. I'll continue to think about it, although I have some interesting implications already.
The voter ranks candidates. Equal ranking and truncation are permitted. RANKING A CANDIDATE IMPLIES APPROVAL, while not ranking a candidate implies disapproval. (In other words, you cannot rank the candidates that you disapprove.) Two matrices are calculated. One is the standard Condorcet matrix, where the value in row x, column y is the number of ballots on which X was ranked, and Y was either ranked lower or not ranked at all. To this is added the second matrix, where the value in row x, column y is the number of ballots on which X was ranked and Y was not ranked. Apply a Condorcet method to the resulting matrix to find the winner. What follows are final matrices which are options for a single voter whose preference order is A>B>C>D>E. Voting A>B>C>D>E under standard Condorcet (not this hybrid method): a b c d e a . 1 1 1 1 b 0 . 1 1 1 c 0 0 . 1 1 d 0 0 0 . 1 e 0 0 0 0 . Voting A>B>C>D (E unranked) under this hybrid system: a b c d e a . 1 1 1 2 b 0 . 1 1 2 c 0 0 . 1 2 d 0 0 0 . 2 e 0 0 0 0 . Notice that the least preferred, E, is inherently hurt worse than under standard Condorcet. To make up for the defeat by A, for instance, E must be ranked above A on *two* ballots, or one ballot if A is unranked (disapproved). Voting A>B>C (DE unranked): a b c d e a . 1 1 2 2 b 0 . 1 2 2 c 0 0 . 2 2 d 0 0 0 . 0 e 0 0 0 0 . The voter gives up the pleasure of ranking D over E, in order to give A, B, and C an extra boost over D. Voting A>B (CDE unranked): a b c d e a . 1 2 2 2 b 0 . 2 2 2 c 0 0 . 0 0 d 0 0 0 . 0 e 0 0 0 0 . Same thing. A and B get an additional boost against C. Voting A (BCDE unranked): a b c d e a . 2 2 2 2 b 0 . 0 0 0 c 0 0 . 0 0 d 0 0 0 . 0 e 0 0 0 0 . Bullet-voting. The voter gives up all ranking influence in order to help A as much as possible. I think there are some things to be said for this system. Truncation can actually be in your interests. It's arguably more expressive, although you could have a dispute there: Is it more important to be able to rank all candidates, or to express disapproval? The following example and resolution reminds me of something Saari suggested here once: 60: A>B (C unranked) 40: B (AC unranked) A wins on the Condorcet matrix, but B wins on the Approval matrix and also on the whole. (Don't forget that next time, the A>B voters can defend against this result if they want.) The B victory looks like a violation of Mutual Majority. Any thoughts? Kevin Venzke [EMAIL PROTECTED] ___________________________________________________________ Do You Yahoo!? -- Une adresse @yahoo.fr gratuite et en français ! Yahoo! Mail : http://fr.mail.yahoo.com _______________________________________________ Election-methods mailing list [EMAIL PROTECTED] http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com
