Majority-efficiency and competition-efficiency in a binary policy model

We introduce a general framework in which politicians choose a (possibly infinite) sequence of binary policies. The two competing candidates are exogenously committed to particular actions on a subset of these issues, while they can choose any policy for the remaining issues to maximize their winning probability. Citizens have general preferences over policies, and the distribution of preferences may be uncertain. We show that a special case of the model, the weighted-issue model, provides a tractable multidimensional model of candidate competition that can generate (i) policy divergence in pure and mixed strategies, (ii) adoption of minority positions, and (iii) inefficient outcomes.