The wasted vote phenomenon with uncertain voter population

Abstract

Palfrey (A mathematical proof of Duvergers law, 1989) shows that in large electorates with deterministic voter population, the expected equilibrium vote share of the weakest party tends to zero asymptotically. We extend this result to the uncertain case where the number of valid votes is a random variable satisfying a mild condition. Special cases include the degenerate, Poisson, binomial, and negative binomial distributions. In particular, we demonstrate that no matter how the number of valid votes fluctuates, as the probability of having a large number of valid votes approaches one, the expected equilibrium vote shares of the weak parties are asymptotically negligible. © 2010 Springer-Verl..