Market Design with Distributional Objectives

We provide optimal solutions to an institution that has distributional objectives when choosing from a set of applications based on merit (or priority). For example, in college admissions, administrators may want to admit a diverse class in addition to choosing students with the highest qualifications. We provide a family of choice rules that maximize merit subject to attaining a level of the distributional objective. We study the desirable properties of choice rules in this family and use them to find all subsets of applications on the Pareto frontier with respect to the distributional objective and merit. In addition, we provide two novel characterizations of matroids.

History: This paper has been accepted for the Mathematics of Operations Research Special Issue on Market Design.

Funding: F. Kojima was supported by the Japan Society for the Promotion of Science [Grant-in-Aid 21H04979] and the Japan Science and Technology Agency [Grant JPMJER2301]. I. E. Hafalir, F. Kojima and M. B. Yenmez were supported by an ARC Discovery Project (DP240101561).