The theory of repeated games offers a compelling rationale for cooperation in a variety of environments. Yet, its consequences for collective decision-making have been largely unexplored. In this paper, we propose a general model of repeated voting and study equilibrium behavior under alternative majority rules. Our main characterization reveals a complex, non-monotonic, relationship between the majority threshold, the preference distribution, and the optimal equilibrium outcome. In contrast with the stage-game equilibrium, the optimal equilibrium of the repeated game involves a form of implicit logroll, individuals sometimes voting against their preference to achieve the efficient decision. In turn, this affects the optimal voting rule, which may significantly differ from the optimal rule under sincere voting. The model provides a rationale for the use of unanimity rule, while accounting for the prevalence of consensus in committees which use a lower majority threshold.