A general probabilistic spatial theory of elections

In this paper, we construct a general probabilistic spatial theory of elections and examine sufficient conditions for equilibrium in two-candidate contests with expected vote-maximizing candidates. Given strict concavity of the candidate objective function, a unique equilibrium exists and the candidates adopt the same set of policy positions. Prospective uncertainty, reduced policy salience, degree of concavity of voter utility functions, some degree of centrality in the feasible set of policy locations, and restrictions on the dimensionality of the policy space are all stabilizing factors in two-candidate elections.3. CITIZEN. We have been called so of many, not that our heads are some brown, some black, some auburn, some bald, but that our wits are so diversely colored. And truly I think if all our wits were to issue out of one skill, they would fly east, west, north, south, and their consent of one direct way should be at once to all points o' the compass. (Shakespeare, coriolanus II.iii. 19–26)