Oops. Need to show that if S_A is negative, one of the S_Aj will be more negative. Haven't done so. Without that, clone independence isn't proved. Back to the drawing board.
--- On Sun, 2/3/13, Ross Hyman <rahy...@sbcglobal.net> wrote: > From: Ross Hyman <rahy...@sbcglobal.net> > Subject: Re: clone independent modification of Baldwin > To: election-meth...@electorama.com > Date: Sunday, February 3, 2013, 9:22 PM > 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 <rahy...@sbcglobal.net> > wrote: > > > From: Ross Hyman <rahy...@sbcglobal.net> > > Subject: clone independent modification of Baldwin > > To: election-meth...@electorama.com > > 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
