Why would a political elite voluntarily dilute its political power by extending the voting franchise? This paper develops a dynamic recursive framework for studying voter enfranchisement. We specify a class of 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 a capital stock, a public good, or the likelihood of an insurrection. Policies are determined by a pivotal decision maker in a potentially restricted franchise. The pivotal decision maker can also delegate decision authority to a new decision maker in the subsequent period. We describe conditions under which an equilibrium of this "dictator delegation game" corresponds to a majority vote decision by the enfranchised group to expand the set of citizens with voting rights. Under these conditions, each period's pivotal decision maker is a median voter who can designate authority to a new median of a larger voting franchise in the next period. We characterize the equilibria by their 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 for 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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