Adaptive Priority Mechanisms

We study a model in which an authority wishes to allocate scarce resources to high-scoring agents while caring about the composition of the allocated agents' characteristics. The key challenge facing the authority is uncertainty about the joint distribution of agents' scores and characteristics. We introduce adaptive priority mechanisms (APM) that prioritize agents based on their scores and their rank relative to others with the same characteristics. We show that APM uniquely implement the ex post optimal allocation. The ubiquitous priority and quota mechanisms are optimal if and only if knife-edge conditions on preferences are satisfied—the authority must be risk-neutral or extremely risk-averse over diversity, respectively. With multiple authorities, Deferred Acceptance implements the unique stable matching when all authorities use the optimal APM. We provide a practical roadmap for implementing APM as a market-design solution and illustrate the gains from APM in a proof-of-concept application to the Chicago Public Schools system.