The evolution of collective choice under majority rules

A collective choice (or opinion) supported by a majority of individuals is challenged recurrently by a new one in a society. We consider a long-run evolution of collective choice under majority rules by stochastic evolutionary game theory. 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 rules belong to the top cycle set. In a multidimensional choice problem where the top cycle set tends to become the whole policy space, a long-run equilibrium belongs to the min–max policy set if the core is non-empty. We show that stochastic evolutionary game theory can mitigate the indeterminacy problem in social choice.