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 to 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 distribution of preferences, turnout increases and then

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... eases when we move from a more proportional to a less proportional system; turnout is maximized for an intermediate degree of proportionality. Moreover, we generalize the competition effect, common to models of endogenous turnout: given the institutional environment, turnout increases in the ex-ante closeness of the election, and more so when the overall system is close to winner take all. These results are robust to a wide range of modeling approaches, including ethical voter models, voter mobilization models, and rational voter models. -Pages for helpful comments and interesting discussions. Comments and suggestions by three anonymous referees are also gratefully acknowledged. The usual disclaimer applies.