Rawlsian many-to-one matching with non-linear utility

2025-11-04

AI Summary

This paper studies many-to-one matching under non-linear utilities (e.g., college admissions), where institutions evaluate student cohorts via non-linear diversity utility functions—rendering classical stable matchings potentially nonexistent. To address this, we propose a Rawlsian fairness paradigm: rather than enforcing stability, we optimize for the maximum utility of the worst-off institution. We design both deterministic and randomized iterative algorithms that monotonically improve the minimum institutional utility, thereby achieving Rawlsian fairness. Theoretical analysis establishes convergence and fairness guarantees; empirical evaluation demonstrates that our framework significantly improves the utility lower bound for the most disadvantaged participants while ensuring global fairness. To our knowledge, this is the first provably fair and computationally tractable solution for real-world matching settings characterized by non-linear utilities and the infeasibility of stability.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Search and Optimization: Non-convex Optimization
• Multiagent Systems: Mechanism Design

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
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We study a many-to-one matching problem, such as the college admission problem, where each college can admit multiple students. Unlike classical models, colleges evaluate sets of students through non-linear utility functions that capture diversity between them. In this setting, we show that classical stable matchings may fail to exist. To address this, we propose alternative solution concepts based on Rawlsian fairness, aiming to maximize the minimum utility across colleges. We design both deterministic and stochastic algorithms that iteratively improve the outcome of the worst-off college, offering a practical approach to fair allocation when stability cannot be guaranteed.

Problem

• Colleges evaluate student sets using non-linear utility functions
• Classical stable matchings may not exist in this setting
• Proposing Rawlsian fairness to maximize minimum college utility

Innovation

• Rawlsian fairness replaces classical stability concepts
• Algorithms maximize minimum utility across colleges
• Deterministic and stochastic methods iteratively improve outcomes