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? We propose a new class of adaptive priority mechanisms (APM) that prioritize agents as a function of both scores (reflecting match quality) and the socioeconomic characteristics of the assigned agents (reflecting diversity). For a single authority with separable preferences over scores and characteristics, we derive an APM that is optimal, generates a unique outcome, and depends solely on the authority's preferences. 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. With many authorities, it is dominant for each of them to use the optimal APM, and each so doing implements the unique stable matching. Using data from Chicago Public Schools, we benchmark the gains from adopting APM and find that they may be considerable.

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

JEL Classification: C78, D47, D61