On Mon, Nov 17, 2008 at 2:35 PM, Kristofer Munsterhjelm <[EMAIL PROTECTED]> wrote: > That rule would admit more sets than the DPC. Call the candidates that a > Droop quota supports above the others, "Droop CWs". Your criterion basically > says "if you're picking k winners, and there are at least k Droop CWs, all > the winners have to be Droop CWs; if there are less than k Droop CWs, those > have to be included in the winning set".
I am not 100% sure that is equivalent to what I suggested, but seems reasonable. > I guess that shouldn't surprise us; since Condorcet doesn't imply Mutual > Majority, a multiwinner Condorcet criterion wouldn't imply the DPC either. > However, the failure mode is different. Condorcet fails MM only when there's > no CW (and the Condorcet criterion can't say which candidate you should > elect); however, this fails even when there are Droop CWs (since we know > Condorcet and the DPC is incompatible, and that a Condorcet winner must also > be a Droop CW). Well, it fails multi-winner condorcet when there isn't enough Droop CWs. The difference in the single winner case is that only a single winner is required. > So we may need a Smith set, and that set would have to be defined so that > electing from it implies DPC. I have no idea how it would actually be > defined, though. Maybe, base it on Copeland; A candidate shall be deemed to defeat an outcome if he is preferred to all winning candidates in the outcome by a Droop quota. The final outcome must be one of the outcomes which ties for fewest defeats. ---- Election-Methods mailing list - see http://electorama.com/em for list info