[EM] clone independent modification of Baldwin

Ross Hyman rahyman at sbcglobal.net
Mon Feb 4 10:13:40 PST 2013

```Silly me.  Try this:
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_B is the score for candidate A.  The V_B 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.

If there is a Condorcet winner it will have a non-negative score.  Also the weighted average of S_A, sum_A (V_A/V_Tot) 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 the weighted average over the clones sum_i (V_Ai/V_A)S_Ai = S_A so some of the clones will have a higher score than the original A and some less (unless they all exactly equal S_A).  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.

```