Just realized silly mistake. S_A1+SA2+SA3 etc = S_A does not mean that some S_Aj have to be above S_A and some below S_A. Does not effect clone independence.
--- On Sun, 2/3/13, Ross Hyman <[email protected]> wrote: > From: Ross Hyman <[email protected]> > Subject: clone independent modification of Baldwin > To: [email protected] > Date: Sunday, February 3, 2013, 8:42 PM > 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
