[EM] clone independent modification of Baldwin

Ross Hyman rahyman at sbcglobal.net
Sun Feb 3 18:42:23 PST 2013

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.