Distributional Preferences for Market Design
Federico Echenique, Teddy Mekonnen, M. Bumin Yenmez
TL;DR
The paper presents a general axiomatic framework for distributional preferences in market design, modeling preferences over sets of agents and identifying three key properties—upper-bound, maximizer, and improvement—that guarantee tractable, globally optimal frontiers with matroid structure. It shows that a greedy distributional choice rule $\mathsf{Ch}^{\pi}$ realizes non-wastefulness and promotion, and that, in centralized markets, the induced deferred-acceptance mechanism is unique under standard requirements and strategy-proofness. The theory unifies canonical policies like reserves and overlapping reserves under partition, transversal, and vector matroids, while also accommodating floors/ceilings and discrete-concavity through the $q$-ordinal concavity of diversity indices. These results provide a coherent, scalable foundation for implementing complex distributional objectives in one- and two-sided markets, resolving path-independence issues that arise with traditional slot-based approaches. The framework thus broadens the design space for diversity and priority objectives in school choice and similar allocation problems, with strong theoretical guarantees grounded in matroid theory.
Abstract
We develop a general framework for incorporating distributional preferences in market design. We identify the structural properties of these preferences that guarantee the path independence of choice rules. In decentralized settings, a greedy rule uniquely maximizes these preferences; in centralized markets, the associated deferred-acceptance mechanism uniquely implements them. This framework subsumes canonical models, such as reserves and matroids, while accommodating complex objectives involving intersectional identities that lie beyond the scope of existing approaches. Our analysis provides unified axiomatic foundations and comparative statics for a broad class of distributional policies.