Strategyproof Choice of Acts: Beyond Dictatorship

We model uncertain social prospects as acts mapping states of nature to (public) outcomes. A social choice function (or SCF) assigns an act to every profile of subjective expected utility preferences over acts. A SCF is strategyproof if no agent ever has an incentive to misrepresent her beliefs about the states of nature or her valuation of the outcomes; it is ex-post efficient if the act selected at any given preference profile picks a Pareto-efficient outcome in every state of nature. We offer a complete characterization of all strategyproof and ex-post efficient SCFs. The chosen act must pick the most preferred outcome of some (possibly different) agent in every state of nature. The set of states in which an agent's top outcome is selected may vary with the reported belief profile; it is the union of all the states assigned to her by a collection of constant, bilaterally dictatorial, or bilaterally consensual assignment rules.