The Implementation of Social Choice Rules: Some General Results on Incentive Compatibility

Abstract

We shall assume that the objectives of a society are embodied in a certain social choice rule. A social choice rule (SCR) selects a set of feasible social states for each possible configuration of individual preferences and other characteristics. One interprets the choice set as the set of welfare optima. For example, given an Arrow social welfare function which embodies individual preferences in a social ordering, then a natural social choice rule is derived by maximizing this social ordering over the feasible set. Alternatively, the Pareto rule is the social choice rule which selects all Pareto efficient states, given individual preferences and the feasible set. These are two particular social choice rules which have received much attention, but our discussion will cover social choice rules in general. If the relevant characteristics of individual agents, such as preferences, happen to be publicly known, then the social choice rule can be implemented trivially because the choice set itself is known. The problem of incentive compatibility arises precisely because these characteristics are not known by the planner a priori. The planner may attempt to learn characteristics directly by asking agents to reveal them. In general, however, if the agents realize how the information they reveal is to be used, they will have an incentive to misrepresent. Then the task of the planner in implementing the social choice rule is more difficult. Obviously, he must use a planning mechanism of some kind, whose outcomes are possible social states. We shall assume that, when he devises the mechanism, the planner knows what social states are feasible, so that he can ensure that the final outcome is feasible. (See, however, Hurwicz, Maskin and Postlewaite (1978), which considers the more general problem where feasibility itself depends on unknown characteristics.) The planner, however, relies on signals from the individual agents to help him implement the social choice rule. It is assumed that each individual agent sends his own signal. The planner's mechanism is then a rule which specifies a social state for each list of signals sent by the individual agents. It is assumed that each agent knows the precise form of the mechanism the planner is using. Then each agent realizes that he is involved in a game, because the outcome of the mechanism depends on the signals which he and all the other