Compulsory Voting: A Mathematical Analysis

Abstract

To address the policy question of whether a country should adopt compulsory voting, this thesis develops a novel mathematical framework for evaluating the trade-offs between compulsory and voluntary voting. We use a heterogeneous preference model with costly voting to quantify the social-welfare implications of both systems. Our analysis reveals that, although compulsory voting incurs higher participation costs, it can elect a more representative candidate---particularly when socioeconomic disparities cause voting costs to be correlated with candidate preference. By deriving social-welfare equations, we identify the conditions under which a switch to compulsory voting is beneficial; namely, when the benefit of electing a more representative candidate exceeds the additional voting costs. Furthermore, we extend the framework to capture the dynamics of close elections and polarization, enhancing the model's realism. In doing so, we account for how ideological divides affect voter turnout and election outcomes. Finally, we apply our model to analyze U.S. presidential elections, providing an empirical example that demonstrates its real-world applicability. Overall, this thesis provides a quantitative foundation for policymakers considering electoral reform.