I wrote a blog post a while back about equilibrium strategies in elections. I defined a "cabal equilibrium" as one in which, not only does no single player wish to change strategies, but no group of players wishes to change strategies together.

For example, (D,D) is not a cabal equilibrium in PD, because both players would prefer to change strategies together to (C,C). But (C,C) is not a cabal equilibrium either, because either player would prefer to change to D. PD has no cabal equilibria.

Elections have cabal equilibria iff there's a Condorcet winner, and a cabal equilibrium elects the Condorcet winner.