Dear Mike, I wrote (28 March 2005): > Suppose V is the number of voters. > > Suppose d[X,Y] is the number of voters who > strictly prefer candidate X to candidate Y. > > Suppose p(z)[X,Y] is the strength of the strongest > path from candidate X to candidate Y when the strength > of a pairwise defeat is measured by "z" (e.g. "z" = > "margins", "z" = "winning votes", "z" = "votes against"). > > Then I proposed the following criterion in 1997: > > If p(wv)[A,B] > V/2 and p(wv)[B,A] < V/2, > then candidate B must be elected with zero > probability. > > Steve Eppley proposed the following criterion in 2000: > > If d[A,B] > V/2 and p(wv)[B,A] < V/2, > then candidate B must be elected with zero > probability.
You wrote (29 March 2005): > Yes, but to outdo a majority pairwise vote, it's necessary > for that MPV to be in a cycle of MPVs _all of which are at > least as strong as it is_. In 1997, I proposed the following method (Schulze method, Schwartz sequential dropping, cloneproof Schwartz sequential dropping, beatpath method, beatpath winner, path voting, path winner): If p(z)[A,B] > p(z)[B,A], then candidate B must be elected with zero probability. Markus Schulze ---- Election-methods mailing list - see http://electorama.com/em for list info