Pareto efficiency with different beliefs

Pareto efficiency is not as compelling when people hold different beliefs as it is under common beliefs or certainty. In the present paper we propose to restrict the standard Pareto relation by imposing the following constraint: in order for one allocation to dominate another, all agents must prefer the former to the latter according to each agent’s belief. In contrast to this unanimity Pareto criterion, the no-betting Pareto concept suggested elsewhere by Gilboa, Samuelson, and Schmeidler supplements the standard Pareto relation with the requirement that there should exist a single hypothetical belief under which all agents prefer the former to the latter. This paper analyzes and compares these and other definitions.