Two results about generic non cooperative voting games with plurality rule

In this paper, we prove that for generic (non cooperative) voting games under plurality rule an equilibrium that induces a mixed distribution over the outcomes (i.e. with two or more candidates elected with positive probability) is isolated. From that we deduce also that the set of equilibrium distributions over outcomes is finite. Furthermore, we offer an example (due to Govindan and McLennan) that shows the impossibility of extending such results to a general framework.