🤖 AI Summary
This paper addresses the dual-objective optimization problem of simultaneously ensuring diversity and selecting high-ability candidates—e.g., in university admissions—by maximizing aggregate candidate quality subject to a given diversity constraint.
Method: We formulate this trade-off as a Pareto frontier search problem and, for the first time, provide two novel axiomatizations grounded in matroid theory. Integrating combinatorial optimization with mechanism design, we develop an algorithmic framework capable of both satisfying hard diversity constraints and enumerating the complete Pareto-optimal set.
Contribution/Results: Our method exactly computes all diversity–quality Pareto-optimal subsets, accompanied by theoretical guarantees of optimality. It establishes a rigorous mathematical foundation for designing fair, transparent, and verifiable selection algorithms—advancing principled approaches to equitable resource allocation under structural constraints.
📝 Abstract
We provide optimal solutions to an institution that has dual goals of diversity and meritocracy when choosing from a set of applications. 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 class of choice rules that maximize merit subject to attaining a diversity level. Using this class, we find all subsets of applications on the diversity-merit Pareto frontier. In addition, we provide two novel characterizations of matroids.