Hi Kevin, You're right. Copeland has some pretty big issues.
It appears to suffer the same deficiencies as margins-based methods, since Copeland ends up treating a victory of 3%-1% with 96% abstaining as being just as good as some other candidate's 51%-49% victory with 0% abstaining. Below is a proposal I'm throwing out there not as a serious proposal, but as food for thought. It may evolve into a serious proposal, but I'm not optimistic. As Abd alluded to in at least one email, it's possible to have a revised version of Copeland that works differently. For example, it could be possible to not credit a candidate with a victory if they don't receive majority support (called "Copeland Majority" for purposes of this mail). We'll say one point for a win, no points for a loss, tie, or "draw" (where neither candidate gets a majority). Here's what the results of some of the examples we've discussed: ========================================================================== Example 1 -------------------------------------------------------------------------- 49: A 24: B>E 27: C>D>B>E Ordinary Copeland result C: 3-1-0 A: 2-2-0 B: 2-2-0 D: 2-2-0 E: 1-3-0 Winner is C Copeland Majority (Win-Loss-Draw) B: 2-0-2 (beats A and E) E: 1-1-2 (beats A) C: 0-0-4 D: 0-0-4 A: 0-2-2 Winner is B ========================================================================== Example 2 -------------------------------------------------------------------------- 49: A>F 24: B 27: C>G>B Ordinary Copeland result A: 3-1-0 B: 2-2-0 C: 2-2-0 F: 2-2-0 G: 1-3-0 Winner is A Copeland Majority: A: 0-1-3 B: 2-0-2 (beats A and F) C: 0-0-4 F: 0-1-3 G: 0-0-4 Winner is B It's something to think about. Myself, I'm not inclined to advocate Copeland Majority in absence of serious analysis, and I'm not inclined to work on that analysis at this time. I suspect it actually has some nice properties when combined with a good tiebreaker, but don't have anything provable to back up my hunch. Rob On Mon, 2005-09-12 at 00:44 +0200, Kevin Venzke wrote: > Hi, > > I thought about this a bit. Consider this election: > > 49 A > 24 B>E > 27 C>D>B>E > > C has 3 wins, and is the only Copeland winner. > > Woodall's plurality criterion is violated, since there's no way to raise C > in rankings including C so that C has even the first preference count that > A starts with. > > Consider this: > > 49 A>F > 24 B > 27 C>G>B > > A has 3 wins, and is the only Copeland winner. > > Eppley's minimal defense criterion is violated, because there is no way > for the C>G>B voters (with the B voters) to at least elect B, without > insincerely ranking B above G (for a tie with A) or both C and G (to win). > > So when I told Rob I couldn't advocate Copeland unless the tie-breaker > satisfied minimal defense, I was talking about something impossible. > > Kevin Venzke > > > > > > > > ___________________________________________________________________________ > Appel audio GRATUIT partout dans le monde avec le nouveau Yahoo! Messenger > Téléchargez cette version sur http://fr.messenger.yahoo.com > ---- > Election-methods mailing list - see http://electorama.com/em for list info ---- Election-methods mailing list - see http://electorama.com/em for list info