Majority Rule When Voters Like to Win

I analyze symmetric majority rule voting equilibria when voters wish to elect the better candidate and to vote for the winner. When voters care only about the winning candidate (the standard formulation) a unique responsive equilibrium exists. The addition of a desire to win creates multiple equilibria, some with unusual properties. I characterize the efficiency of optimal equilibria as the population becomes large and show that a discontinuity arises in the information aggregation capabilities of the majority rule voting mechanism: in elections without a dominant front-running candidate efficiency can be obtained, whereas in races with a front-runner information cannot be effectively aggregated in equilibrium.