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? ---- Election-Methods mailing list - see http://electorama.com/em for list info
