Binary public decisions and undominated mechanisms

Journal of Economic Theory

A Solomonic solution to the problem of assigning a private indivisible good

Games and Economic Behavior

We discuss the problem of choosing between two public alternatives under the assumption that preferences are quasilinear. We concentrate on the class of strategy-proof, anonymous and feasible mechanisms that are not dominated by another strategy-proof, anonymous and feasible mechanism. We characterize the class of Undominated mechanisms that exhibit a minimal degree of impartiality toward the two alternatives and that do not allow for positive transfers to agents whose preferred alternative is selected. The novelty of the solution we propose lies in the fact that it affords the mechanism designer multiple ways to resolve the issue of the public decision and uniquely determines the design of transfers based on this choice.

A benevolent Planner wishes to assign an indivisible private good to n claimants, each valuing the object differently. Individuals have quasi-linear preferences. Therefore, the possibility of transfers is allowed. A second-best efficient mechanism is a strategy-proofand anonymous mechanism that is not Pareto dominated by another strategy-proof and anonymous mechanism. In this context, we identify three conditions that are necessary and, together with Voluntary Participation, sufficient for a mechanism to be second-best efficient. This set includes mechanisms that destroy the good at certain profiles. For domains comprising two individuals we provide an explicit characterization of the family of second-best efficient mechanisms.