Is there a really good, decisive, general purpose, tie breaking order that depends on chance only is case of complete symmetry? Here's one that's better than nothing: Let Top( X) be the percent of ballots on which X is not outranked by a Y candidate. Let Bot(X) be the percentage of ballots on which X outranks no candidate. The suggest tie breaking order is given by the formula ... F(X)=(Top(X)-Bot(X))/(200%-Top(X)-Bot(X)), primarily, and secondarily by just the numerator of F(X). The only case that this does not handle well is the case where F is zero for the tied alternatives. Is there a nice way to invoke the pairwise wins in that case? If we had a good enough Universal Tie Resolution Order, we could use it as a standard, default agenda for all of our agenda based methods, including Agenda Based Chain Climbing, which would open up the UD umbrella to Banks efficient methods! -Forest