Here is a clone independent modification of Baldwin. Has this been discussed before?
V_A>B is the number of ballots that rank A above B. V_A is the number of ballots that rank A at the top. S_A = sum_B (V_A>B - V_B>A)V_A V_B is the score for candidate A. The V_AV_B factor makes it a modification of Baldwin. Eliminate the candidate with lowest score. Recalculate V_A's and S_A's. Repeat until one candidate remains. Like Baldwin, if there is a Condorcet winner it will have a positive score. Also like Baldwin sum_A S_A =0 so that if there is a Condorcet winner it is guaranteed that there will be at least one other candidate with negative score so the Condorcet winner will not be eliminated. It is clone independent because S_A does not change if one of the other candidates is cloned. If A is cloned to A1,A2 etc. then S_A1+SA2+SA3 etc = S_A so some of the clones will have a higher score than the original A and some less. This might mean that one of the clones of A would be eliminated before A would have been, but since other clones of A remain, and we are eliminating just one at a time, everything is ok. I do not think that the Nanson version of this would always be clone independent, but I haven't checked. I think that for Nanson it might be possible that S_A is negative so would be eliminated but when cloned, one of the clones could have positive score and remain after the elimination step and possibly win the election. ---- Election-Methods mailing list - see http://electorama.com/em for list info
