Bargaining foundations of the median voter theorem

We provide strong game-theoretic foundations for the median voter theorem in a onedimensional bargaining model based on Baron and Ferejohn’s (1989) model of distributive politics. We prove that, as the agents become arbitrarily patient, the set of proposals that can be passed in any subgame perfect equilibrium collapses to the median voter’s ideal point. While we leave the possibility of some delay, we prove that the agents’ equilibrium continuation payoffs converge to the utility from the median, so that delay, if it occurs, is inconsequential. We do not impose stationarity or any other refinements. Our result counters intuition based on the folk theorem for repeated games, and it contrasts with the known result for the distributive bargaining model that, as agents become patient, any division of the dollar can be supported as a subgame perfect equilibrium outcome. ∗The authors thank Hülya Eraslan, Nolan McCarty, Adam Meirowitz, Dave Primo, and Ronny Razin for their helpful comments. Support from the National Science Foundation, grant number SES-0213738, is gratefully acknowledged.