Given: 25 A>B>C 49 B>A>C 26 C>A>B
A is Condorcet winner. Say all members of faction vote same way, so there are 3 players. Say 25 vote A and B, 49 vote B, 26 vote C. B wins. If the A>B>C faction withdraws its support for B then B still wins. If the C faction also votes for A candidate B still wins. This is a Nash equilibrium that did not elect the Condorcet candidate. Nash equilibria and the existence of Condorcet winners have no definitive link, although I suspect that if you enumerated all possible Nash equilibria for any situation (treating all factions as single players) most Nash equilibria would elect the CW. Still, everything I said 24 hours ago was bull. Alex
