The Evolution of Collective Choice Under Majority Rule

Abstract

We consider a dynamic process of collective choice under majority rule in which a status quo policy evolves. The analysis is based on stochastic evolutionary game theory and relates the static solution concepts of social choice theory to a long-run equilibrium in a dynamic voting process. The Condorcet winner is uniquely a long-run equilibrium for all (super-)majority rules. When the Condorcet winner does not exist, the long-run equilibria under all majority voting rules belong to the top cycle of policies under a simple majority. When the policy space is multidimensional and the voting quota is larger than the min-max quota, the long-run equilibrium belongs to the min-max set. Finally, the Borda winner appears as a long-run equilibrium under unanimity if voters’ behavior is governed by a logit choice rule.

Keywords: Collective choice, Voting, Stochastic evolutionary game theory, Condorcet winner, Borda winner