I tried two more examples at Rob's Condorcet Demo site: The demo claimed the result of 46:1 20:2 34:3>2>1 is a two-way tie since two candidates have a largest opposition of 46. But that's not the same method as the Condorcet we've defined here, which counts only opposition in pair *defeats*. Candidate #2's "46 opposed" were in a pairwin and should not be counted. The method Rob has implemented was discussed in EM a little. The demo correctly showed all three candidates are in the Smith set, but it doesn't go the extra step and show the Smith//Condorcet winner. That would be a useful addition to the demo, and easy to do. The other example I tried was: 46:1 20:2 joker 34:3>2>1 The 20 ballots with the "joker" characters were invalidated. I'd appreciate it if Rob would modify his code so that extra characters at the end of a ballot won't invalidate it. This would allow users to append names or handles to their ballots, which would help voters verify their ballots were correctly entered. ---Steve (Steve Eppley [EMAIL PROTECTED])