Inequity Aversion May Increase Inequity

Abstract

Inequity aversion models have been used to explain equitable payoff divisions in bargaining games. I show that inequity aversion can actually increase the asymmetry of payoff division if unanimity is not required. This is because responders may be willing to accept a lower share rather than risk being left out. Inequity aversion may also affect comparative statics: the advantage of being the proposer can decrease as players become more impatient. Game theory usually assumes that players care only about their own material payoffs. This hypothesis is clearly refuted by the experimental evidence in the ultimatum and related games; see Camerer (2003) for a recent survey. Inequity aversion theories have been developed in order to account for the stylised facts observed in the laboratory; see Fehr and Schmidt (1999) and Bolton and Ockenfels (2000). Inequity aversion means that people are willing to give up some material payoffs in order to achieve more equitable outcomes. Inequity averse responders prefer to reject small offers in the ultimatum game, and the proposers, anticipating this, make higher offers. In this article I examine the implications of inequity aversion for bargaining games in which unanimity is not required (e. g., legislative bargaining games) and show that it may lead to a more inequitable outcome than would occur with selfish preferences. The leading model of legislative bargaining is due to Baron and Ferejohn (1989). In this model, n symmetric players must divide a budget by simple majority. Each player has an equal chance of being chosen to propose a division of the budget. Once a proposal is made, the remaining players vote 'yes' or 'no'; if a majority of the players supports the proposal it is implemented and the game ends; otherwise the procedure is repeated. This model predicts that minimal winning coalitions will form and that the proposer will receive a disproportionate share of the proceedings. Thus, the equilibrium of the Baron-Ferejohn model with selfish preferences exhibits a substantial amount of inequity: some players are excluded (almost half of them if the decision rule is simple majority), and the proposer receives a substantial share (more than half of the total payoff if the decision rule is simple majority). The advantage of the proposer increases as players become more impatient or more risk averse. The Baron-Ferejohn model has led to many applications and extensions.1 In its simplest form, it assumes that parties are selfish, risk neutral and only concerned with their share of cabinet posts as opposed to policy. The predictions of the model under these assumptions have been tested by Ansolabehere et al. (2005) using data on the