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_. I wrote (29 March 2005): > 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. You wrote (30 March 2005): > SSD and CSSD are two different methods, which can give two > different outcomes with the same ballot-set. So BeatpathWinner > can't be both SSD and CSSD. > > BeatpathWinner is equivalent to CSSD, but not to SSD. > > I mention that for your information, so that, if you want to > be correct, you can leave SSD out of the list of names that > refer to BeatpathWinner or methods equivalent to it. But it > isn't important, and, as I said, I mention it only for your > information. BeatpathWinner _is_ SSD _is_ CSSD in so far as all of them share this property: If p(z)[A,B] > p(z)[B,A], then candidate B must be elected with zero probability. If you don't agree with this then please post an example where this is not true. Markus Schulze ---- Election-methods mailing list - see http://electorama.com/em for list info