Cooperation and punishment under repeated majority voting

In light of the extensive theoretical evidence suggesting absence of equilibrium in voting models, Tullock (1981) asks "Why So Much Stability?" Our results suggest the following answer: Political agents engaged in long-term relationships can sustain highly stable allocations if there are strongly held norms for punishment of defectors. Moreover, recent work by Cremer (1986) suggests that even if decisionmakers have finite horizons, significant cooperation is nevertheless feasible if institutions are indefinitely-lived. Our results show that a wide range of allocations can be sustained as equilibria by the threat of political banishment. The following anecdote suggests that something like a political banishment punishment has in fact been employed in practice: "Senator James L. Buckley...tried to delete forty-four public works projects at the committee stage in the Senate. The members voted down all his amendments except the ones cutting out projects in New York; these latter they adopted." Quoted from Mayhew (1974, pp. 91–92) who cites Reeves (1974) Ferejohn (1974, p. 114) cites an example in which Senator Proximre was similarly punished for supporting proposals to cut appropriations for the Department of the Interior—a House-Senate Conference Committee deleted the Senator's favored project from the Interior appropriations bill. Our results indicate not only that stable cooperative outcomes are possible but also that a wide range of allocations can be sustained. This is a liability rather than an asset; the theory provides weak predictions. One way to augment the model is to assume that the chosen contract is a member of the ex ante optimal set of feasible contracts. This assumption can be expected to give strong predictions. In our model, when the conditions of Proposition 3 are satisfied, the assumption that the ex ante optimal contract is chosen leads to a prediction of equal division of the cake each period. The assumption that the ex ante optimal contract is chosen is a natural one when agreements are indeed made "behind the veil of ignorance"; under such conditions the ex ante optimal contract would receive unanimous support. When individuals are differently situated at the time contracting occurs, the assumption of ex ante optimality of the contract might better be replaced by a characterization of the bargaining problem individuals confront in attempting to agree upon a contract. The analysis of Baron and Ferejohn (1986) is in this spirit. Our model has two related features, both of which may seem unrealistic: The punishment for defection from a cooperative agreement is eternal banishment, and punishment never occurs. Both features are inconsistent with at least the second of our two anecdotes. Less severe punishments than eternal banishment could no doubt be devised, e.g., temporary banishment. However, the range of cooperative agreements that could be supported by the weaker punishment would be smaller, and defection from agreements that would be supported by the weaker punishment would never occur. Thus, while a weaker punishment might seem more "realistic," the introduction of such a punishment in the current framework is artificial and does not alter the prediction that punishment never occurs in equilibrium. Similar problems arise in models of self-enforcing private agreements when there is neither uncertainty nor private information. To address these problems, Green and Porter (1984) developed a model of cartel enforcement with uncertainty and private information in which punishment occurs, and Abreu, Pierce, and Stachetti (1986) have shown that the optimal punishment period in the Green-Porter model is finite. (See also Porter (1983).) In the Green-Porter model, an unobserved random shock introduces variation in outcomes. However, since the shock is unobserved and individual actions are private information, the players cannot tell whether the variation is due to the random shock or to a defection by another player. If a sufficiently adverse outcome occurs, the punishment regime is invoked. However, since the punishment regime may (and in equilibrium will) be triggered by the random shock, it is in the players' interests to engage in a limited period of punishment and then revert to the cooperative regime. The introduction of uncertainty and private information in the model developed in this paper may also motivate occasional finite punishments. If our anecdotes are to serve as a guide, however, the identity of defectors in the political arena will sometimes be known—in contrast to the Green-Porter model in which the identity of defectors cannot be observed. This suggests that a somewhat different motivation for finite, observed punishments will be more appropriate in our setting than in the cartel setting studied by Green and Porter. We view this as a fruitful area for extension of the model. Copyright Martinus Nijhoff Publishers 1987