Hallo, > sorry, but just on the surface this doesn't > seem right. > > for instance, a run-of-the-mill no-cycle Condorcet > case (actually it was IRV and the Condorcet winner > did not win) would be the Burlington 2009 election > most of us are familiar with. in that case M=5. > now if you picked k=3 and chose candidate A to be > Kurt Wright (who was the plurality winner and neither > the IRV winner nor the CW), there is a set of (k-1) > candidates (those would be Smith and Simpson) that > Wright beat consistently. yet he is not the overall > winner. > > you can go to the Warren Smith page or i can scarf > up the numbers from the defeat matrix again. > > how am i reading this wrong? For k=3, this criterion says that, when a candidate wins every 3-way election, then this candidate should also be the overall winner. So to be able to apply this criterion to Kurt Wright, he would also have to win a 3-way election between himself and (say) Montroll and Kiss. Markus Schulze