The authors thank Itai Ashlagi for insightful discussions and suggestions throughout this project and Jack Buckley, Sharad Goel, Josh Grossman, Ramesh Johari, Wanyi Li, Irene Lo, Muriel Niederle, Collin Raymond, Alvin E. Roth, Philipp Strack, Sabina Tomkins, Johan Ugander, Gabriel Weintraub, and anonymous reviewers of Management Science, Association for Computing Machinery Conference on Fairness, Accountability, and Transparency (ACM FAccT) 2021, and Association for Computing Machinery Equity and Access in Algorithms, Mechanisms, and Optimization (ACM EAAMO) 2021 for helpful comments.