I'm sorry to say my original claim is not true. Counterexample:
Sincere Rankings 4 A>B>C 3 B>A>C 2 C>B>A If (in the third faction) B is sufficiently close to C in utility, it is to that faction's advantage to reverse the order of B and C. On the other hand, as long as C has greater utility than B, and epsilon is sufficiently small, the probability distribution (1/9 - epsilon, 1/9 - .75epsilon, 1/9 - .50episilon, ... , 1/9 + epsilon) in place of my original suggestion will do the job. In this example, epsilon < 2*(deltaR)/9 is sufficiently small, where deltaR is the percentage difference in utility between C and B. Forest > > Draw a ballot at random. Use the ranking on this ballot to rank > all of the other ballots from worst to best > according to their favorites. > > Elect the favorite indicated on the k_th ballot with probability > 2*k/(n+n^2) , where n is the number of > ballots. > ---- Election-Methods mailing list - see http://electorama.com/em for list info
