Differences in electoral rules and/or legislative, executive or legal institutions across countries induce different mappings from election outcomes to distributions of power. We explore how these different mappings affect voters' participation in a democracy. Assuming heterogeneity in the cost of voting, the effect of such institutional differences on turnout depends on the distribution of voters' preferences for the parties: when the two parties have similar support, turnout is higher in a winner-take-all system than in a power sharing system; the result is reversed when one side has a larger base. The results are robust to a wide range of modeling approaches, including the instrumental voting model, ethical voter models, and voter mobilization models. Findings from laboratory experiments provide empirical support for most of the theoretical predictions.