[EM] I was wrong

[Alex Small]

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