You're right. I've drawn out the game theory matrix and the honest outcome: 49 C 27 A>B 24 B>A is indeed the stable one, with A winning.
So the only way for B to win is for his supporters to say they are indifferent between A and C and threaten to bullet vote "B". Then the A supporters fall for it and vote "A=B" to prevent C from winning. B wins. I wonder if this is sequence of events is likely at all. ~ Andy On Fri, Dec 9, 2011 at 2:31 PM, Jameson Quinn <jameson.qu...@gmail.com>wrote: > No, the B group has nothing to gain by defecting; all they can do is bring > about a C win. Honestly, A group doesn't have a lot to gain from defecting, > either; either they win anyway, or they misread the election and they're > actually the B's. > > Jameson > > 2011/12/9 Andy Jennings <electi...@jenningsstory.com> > >> Here’s a method that seems to have the important properties that we >>> have been worrying about lately: >>> >>> (1) For each ballot beta, construct two matrices M1 and M2: >>> In row X and column Y of matrix M1, enter a one if ballot beta rates X >>> above Y or if beta gives a top >>> rating to X. Otherwise enter a zero. >>> IN row X and column y of matrix M2, enter a 1 if y is rated strictly >>> above x on beta. Otherwise enter a >>> zero. >>> >>> (2) Sum the matrices M1 and M2 over all ballots beta. >>> >>> (3) Let M be the difference of these respective sums >>> . >>> (4) Elect the candidate who has the (algebraically) greatest minimum >>> row value in matrix M. >>> >>> Consider the scenario >>> 49 C >>> 27 A>B >>> 24 B>A >>> Since there are no equal top ratings, the method elects the same >>> candidate A as minmax margins >>> would. >>> >>> In the case >>> 49 C >>> 27 A>B >>> 24 B >>> There are no equal top ratings, so the method gives the same result as >>> minmax margins, namely C wins >>> (by the tie breaking rule based on second lowest row value between B and >>> C). >>> >>> Now for >>> 49 C >>> 27 A=B >>> 24 B >>> In this case B wins, so the A supporters have a way of stopping C from >>> being elected when they know >>> that the B voters really are indifferent between A and C. >>> >>> The equal top rule for matrix M1 essentially transforms minmax into a >>> method satisfying the FBC. >>> >>> Thoughts? >>> >> >> >> To me, it doesn't seem like this fully solves our Approval Bad Example. >> There still seems to be a chicken dilemma. Couldn't you also say that the >> B voters should equal-top-rank A to stop C from being elected: >> 49 C >> 27 A >> 24 B=A >> Then A wins, right? >> >> But now the A and B groups have a chicken dilemma. They should >> equal-top-rank each other to prevent C from winning, but if one group >> defects and doesn't equal-top-rank the other, then they get the outright >> win. >> >> Am I wrong? >> >> ~ Andy >> >> >> >> ---- >> Election-Methods mailing list - see http://electorama.com/em for list >> info >> >> >
---- Election-Methods mailing list - see http://electorama.com/em for list info