Bargaining Foundations of the Median Voter Theorem.” Typescript

We provide strong game-theoretic foundations for the median voter theorem in a one-dimensional bargaining model based on Baron and Ferejohn’s (1989) model of dis-tributive 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 me-dian 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 re-finements. 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