Policy-motivated candidates, noisy platforms, and non-robustness

A model of a two-candidate election is developed in which the candidates are mainly office-motivated but also to some arbitrarily small extent policy-motivated, and their chosen platforms are to some arbitrarily small extent noisy. The platforms’ being noisy means that if a candidate has chosen a particular platform, the voters’ perception is that she has, with positive probability, actually chosen some other platform. It is shown that (i) an equilibrium in which the candidates play pure exists whether or not there is a Condorcet winner among the policy alternatives, and (ii) in this equilibrium the candidates choose their ideal points, which means that the platforms do not converge.