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 <[email protected]> > 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
