Why would a political elite voluntarily dilute its political power by extending the franchise? This paper develops a dynamic recursive framework for studying voter enfranchisement. We study properties of dynamic enfranchisement games, dynamic games in which political rights evolve over time. Each period, private decisions of citizens co-mingle with government policies to act upon a state variable such as capital stock, a public good, or the likelihood of an insurrection. Policies are determined by the median voter of a potentially restricted franchise. The enfranchised group can choose, through its median voter, to expand the set of citizens with voting rights. In this way, each period's median voter can effectively delegate decision authority to a new median in the next period. We characterize the equilibria of a dynamic enfranchisement game by its Euler equations. In certain games, the equilibria generate paths that display a gradual, sometimes uneven history of enfranchisement that is roughly consistent with observed patterns of extensions. Our main result shows that extensions of the franchise occur in a given period if and only if the private decisions of the citizenry have a net positive spillover to the dynamic payoff of the current median voter. The size of the extension depends on the size of the spillover. Since the class of games we study can accommodate a number of proposed explanations for franchise extension (e.g., the threat of insurrection, or ideological or class conflict within the elite, etc), the result suggests a common causal mechanism in each of these seemingly different explanations. We describe a number of parametric environments that correspond to the various explanations, and show how the mechanism works in each.
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