Candidate quality in a Downsian model with a continuous policy space

This paper characterizes a mixed strategy Nash equilibrium in a one-dimensional Downsian model of two-candidate elections with a continuous policy space, where candidates are office motivated and one candidate enjoys a nonpolicy advantage over the other candidate. We assume that voters have quadratic preferences over policies and that their ideal points are drawn from a uniform distribution over the unit interval. In our equilibrium the advantaged candidate chooses the expected median voter with probability one and the disadvantaged candidate uses a mixed strategy that is symmetric around it. We show that this equilibrium exists if the number of voters is large enough relative to the size of the advantage.