Diversity in Choice as Majorization

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.