Dear Steve, you wrote (7 March 2003): > Minimax(pairwise opposition) even satisfies a criterion promoted by > some advocates of Instant Runoff, which I call "Uncompromising": > > Let w denote the winning alternative given some set > of ballots. If one or more ballots that had only w > higher than bottom are changed so some other > "compromise" alternative x is raised to second > place (still below w but raised over all the other > alternatives) then w must still win. > > The proof that Minimax(pairwise opposition) satisfies Uncompromising > is simple: Raising x increases the pairwise opposition for all > candidates except w and x, and does not decrease the pairwise > opposition for any candidate, so w must still have the smallest > maximum pairwise opposition. > > That criterion can be strengthened somewhat and still be satisfied: > Changing pairwise indifferences to strict preferences in ballots that > ranked w top cannot increase w's pairwise opposition or decrease any > other alternatives' pairwise opposition.
That sounds like Woodall's later-no-harm + later-no-help. (Douglas R. Woodall, "Monotonicity of single-seat preferential election rules," Discrete Applied Mathematics, vol. 77, pp. 81-98, 1997.) In another paper, Woodall proves that no election method can simultaneously meet later-no-harm, later-no-help, monotonicity, and mutual majority. Therefore, the fact that Minimax(pairwise opposition) violates mutual majority in such a drastic manner can be considered a consequence of the fact that it meets later-no-harm, later-no-help, and monotonicity. Example: 20 ABCD 20 BCAD 20 CABD 13 DABC 13 DBCA 13 DCAB You wrote (7 March 2003): > That's why I think the best method is a variation of Ranked Pairs > which I call Maximize Affirmed Majorities, or MAM. In so far as you have always considered Mike Ossipoff to be authoritative, I would like to know what you think about the fact that he doesn't promote Ranked Pairs anymore at his web pages. Markus Schulze _______________________________________________ Election-methods mailing list [EMAIL PROTECTED] http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com
