Diversity in Choice as Majorization

TL;DR

This paper introduces a majorization-based framework for modeling diversity in school admissions, proposing an optimal choice rule that balances diversity and priority while satisfying key economic properties.

Contribution

It generalizes majorization to arbitrary targets and characterizes an optimal $r$-targeting Schur choice rule for diversity and priority in admissions.

Findings

The $r$-targeting Schur choice rule is optimal among all rules.

The rule guarantees no unfilled seats and maintains diversity and priority.

It satisfies path independence and substitutability, ensuring stable matching outcomes.

Abstract

We propose a framework that uses majorization to model diversity and representativeness in school admissions. We generalize the standard notion of majorization to accommodate arbitrary distributional targets, such as a student body that reflects the population served by the school. Building on this framework, we introduce and axiomatically characterize the $r$-targeting Schur choice rule, which balances diversity and priority in admissions. We show that this rule is optimal: any alternative rule must either leave seats unfilled, reduce diversity, or admit lower-priority students. The rule satisfies path independence (and substitutability), which guarantees desirable outcomes in matching markets. Our work contributes to the ongoing discourse on market design by providing a new and flexible framework for improving diversity and representation.