Distributional Preferences for Market Design

Institutions selecting students, employees, or members value both about who is selected and the resulting group's composition. We study ``distributional'' preferences over group composition, and identify an upper-bound property and two exchange properties. With the upper-bound property, the exchange properties are necessary and sufficient for two results: the greedy rule is the unique choice rule that is non-wasteful, distributionally maximal, and free of justified envy; it is also path independent. In matching markets, deferred acceptance is the unique mechanism satisfying the three axioms, individual rationality, and strategy-proofness. Our framework accommodates intersectional identities and subsumes models based on reserves and matroids.