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 of the distributional objective and merit. In addition, we provide two novel characterizations of matroids. A full version is available at https://arxiv.org/abs/2301.00237.

Path independence is arguably one of the most important choice rule properties in economic theory. We show that a choice rule is path independent if and only if it is rationalizable by a utility function satisfying ordinal concavity, a concept closely related to concavity notions in discrete mathematics. We also provide a rationalization result for choice rules that satisfy path independence and the law of aggregate demand. A full version is available at https://arxiv.org/abs/2303.00892.

Equal pay laws increasingly require that workers doing "similar" work are paid equal wages within firm. We study such "equal pay for similar work" (EPSW) policies theoretically and test our model's predictions empirically using evidence from a 2009 Chilean EPSW. When EPSW only binds across protected class (e.g., no woman can be paid less than any similar man, and vice versa), firms segregate their workforce by gender. When there are more men than women in a labor market, EPSW increases the gender wage gap. By contrast, EPSW that is not based on protected class can decrease the gender wage gap.

In a matching market with distributional objectives, we study the existence of mechanisms that weakly improve the distributional objective (compared to a status-quo matching), and satisfy constrained efficiency, individual rationality, and strategy-proofness.

In this paper, we consider two-sided, many-to-one matching problems where agents in one side of the market (schools) impose some distributional constraints (e.g., a maximum quota for a set of schools), and develop a strategyproof mechanism that can handle a very general class of distributional constraints. We assume distributional constraints are imposed on a vector, where each element is the number of contracts accepted for each school. The only requirement we impose on distributional constraints is that the family of vectors that satisfy distributional constraints must be hereditary, which means if a vector satisfies the constraints, any vector that is smaller than it also satisfies them. When distributional constraints are imposed, a stable matching may not exist. We develop a strategyproof mechanism called Adaptive Deferred Acceptance mechanism (ADA), which is nonwasteful and "more fair" than a simple nonwasteful mechanism called the Serial Dictatorship mechanism (SD) and "less wasteful" than another simple fair mechanism called the Artificial Cap Deferred Acceptance mechanism (ACDA). We show that we can apply this mechanism even if the distributional constraints do not satisfy the hereditary condition by applying a simple trick, assuming we can find a vector that satisfy the distributional constraints efficiently. Furthermore, we demonstrate the applicability of our model in actual application domains.

The market design literature has successfully designed mechanisms that achieve desirable properties such as strategy-proofness (incentive compatibility) and efficiency at the allocation stage. However, agents must often make investment decisions before participating in allocation mechanisms. These decisions are endogenous, in the sense that market participants' investments depend on the choice of mechanism.