The vigilant eating rule: A general approach for probabilistic economic design with constraints

We consider probabilistic allocation of objects under ordinal preferences and constraints on allocations. We devise an allocation mechanism, called the vigilant eating rule (VER), that applies to nearly arbitrary constraints. It is constrained ordinally efficient, can be computed efficiently for a large class of constraints, and treats agents equally if they have the same preferences and are subject to the same constraints. When the set of feasible allocations is convex, it is characterized by ordinal egalitarianism. As a case study, we assume objects have priorities for agents and apply VER to sets of probabilistic allocations that are constrained by stability. While VER always returns a stable and constrained efficient allocation, it fails to be strategyproof, unconstrained efficient, and envy-free. We show, however, that each of these three properties is incompatible with stability and constrained efficiency.