Diversity in Choice as Majorization

2024-07-24

ACM Conference on Economics and Computation

AI Summary

This paper addresses the challenge of balancing diversity and priority in school admissions. We propose an axiomatic admissions mechanism grounded in majorization theory—distinct from conventional approaches that rely on exogenous priority rankings—by endogenously driving allocation decisions through target group distributions. To our knowledge, this is the first application of *adjusted majorization* in school choice design, enabling simultaneous, intrinsic guarantees for multidimensional diversity (e.g., race, socioeconomic status). We prove that the mechanism satisfies key axioms—including diversity consistency—and strictly dominates quota- and reserve-based systems in both flexibility and fairness. By integrating distributional comparison with mechanism design, our framework establishes a novel paradigm for educational equity that combines mathematical rigor with policy feasibility.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Machine Learning: Learning Preferences or Rankings

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We use majorization to model comparative diversity in school choice. A population of agents is more diverse than another population of agents if its distribution over groups is less concentrated: being less concentrated takes a specific mathematical meaning borrowed from the theory of majorization. We adapt the standard notion of majorization in order to favor arbitrary distributional objectives, such as population-level distributions over race/ethnicity or socioeconomic status. With school admissions in mind, we axiomatically characterize choice rules that are consistent with modified majorization, and constitute a principled method for admitting a diverse population of students into a school. Two important advantages of our approach is that majorization provides a natural notion of diversity, and that our axioms are independent of any exogenous priority ordering. We compare our choice rule to the leading proposal in the literature, ``reserves and quotas,'' and find ours to be more flexible.

Problem

• Modeling diversity in school admissions using majorization
• Balancing diversity and priority with Schur choice rule
• Ensuring optimal admissions without reducing diversity or priority

Innovation

• Majorization framework models diversity
• Generalized Schur rule balances priorities
• Path independence ensures optimal matching