We study the ability of elections to solve the dynamic programming problem of a representative voter in a dynamic citizen-candidate framework. We assume a finite number of states and general utilities and state transition probability, thereby allowing for non-trivial dynamics. We prove existence of equilibrium; we show that politicians may manipulate the state to affect their electoral prospects, resulting in suboptimal payoffs for the voter; and we show that for equilibria satisfying a responsive voting condition, equilibria become approximately optimal as the voter becomes patient.