Adaptive Priority Mechanisms

Abstract

How should authorities that care about match quality and diversity allocate resources when they are uncertain of the market they face? Such a question appears in many contexts, including the allocation of school seats to students from various socioeconomic groups with differing exam scores. We propose a new class of adaptive priority mechanisms (APM) that prioritize agents as a function of both scores that reflect match quality and the number of assigned agents with the same socioeconomic characteristics. When there is a single authority and preferences over scores and diversity are separable, we derive an APM that is optimal, generates a unique outcome, and can be specified solely in terms of the preferences of the authority. By contrast, the ubiquitous priority and quota mechanisms are optimal if and only if the authority is risk-neutral or extremely risk-averse over diversity, respectively. When there are many authorities, it is dominant for each of them to use the optimal APM, and each so doing implements the unique stable matching. However, this is generally inefficient for the authorities. A centralized allocation mechanism that first uses an aggregate APM and then implements authority-specific quotas restores efficiency. Using data from Chicago Public Schools, we estimate that the gains from adopting APM are considerable.

Keywords: Matching Theory, Market Design, Allocative Efficiency, Affirmative Action, Instrument Choice

JEL Classification: C78, D47, D61