Electoral competition in heterogeneous districts

This paper considers a model of elections in which parties compete simultaneously for multiple districts. I show that if districts are heterogeneous, then a unique two-party equilibrium exists under plurality rule in which further entry is deterred. The equilibrium requires that parties choose noncentrist policy platforms and not converge to the ideal policy of the median voter. These characteristics are consistent with empirical observation, in contrast to those of single-district models. Necessary and sufficient conditions for the existence of the equilibrium are then characterized and related to Duverger's law. The existence of multiple- party equilibria in this environment is also considered.