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.