Turnout, Polarization, and Duverger's Law

We reexamine the impact of abstention due to alienation on policy outcomes and the choices of strategic candidates. We establish the existence of a unique equilibrium under plurality rule in which only two candidates enter, choose divergent policy positions, and deter subsequent entry. This equilibrium is simultaneously consistent with the dual empirical regularities of Duverger's Law and policy divergence. Driving our results is the observation that when abstention is included, a third candidate optimally enters the election by differentiating himself from the incumbent candidates. This property leads to equilibrium behavior that is different to when full turnout is assumed, and resonates well with observations of entry in real elections. Our results confirm that not only are the platforms of candidates important to the turnout decisions of voters, but that the turnout decisions of voters are important to platform positions. The model provides a causal mechanism linking these two variables, offering a theoretical basis for the decrease in turnout and increase in polarization experienced in the U.S. after the 1960's.