World democracies widely differ in legislative, executive, and legal institutions. Different institutional environments induce different mappings from electoral outcomes to the distribution of power. We explore how these mappings affect voters' participation in an election. We show that the effect of such institutional differences on turnout depends on the distribution of voters' preferences. We uncover a novel contest effect: Given the preferences distribution, turnout increases and then decreases when we move from a more proportional to a less proportional power‐sharing system; turnout is maximized for an intermediate degree of power sharing. Moreover, we generalize the competition effect, common to models of endogenous turnout: Given the institutional environment, turnout increases in the ex ante preferences evenness, and more so when the overall system has lower power sharing. These results are robust to a wide range of modeling approaches, including ethical voter models, voter mobilization models, and rational voter models.