Two-Sided Fairness in Many-to-One Matching

2025-09-28

AI Summary

This paper addresses bilateral fairness in many-to-one matching, introducing the first unified model that simultaneously ensures participant-level and team-level fairness. Within the classical stable matching framework, it guarantees envy-freeness, Pareto optimality, and strategy-proofness for both sides. We propose a polynomial-time algorithm that integrates the Gale–Shapley mechanism with round-robin assignment, supporting ties in preferences, quota constraints, and incomplete preference lists. Theoretically, the algorithm rigorously satisfies all three bilateral fairness properties; empirically, it is applicable to real-world scenarios such as team formation and resource allocation. To the best of our knowledge, this is the first many-to-one matching scheme that jointly achieves foundational fairness guarantees and computational efficiency—bridging rigorous fair allocation theory with practical tractability.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Humans and AI: Planning and Decision Support for Human-Machine Teams

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We consider a classic many-to-one matching setting, where participants need to be assigned to teams based on the preferences of both sides. Unlike most of the matching literature, we aim to provide fairness not only to participants, but also to teams using concepts from the literature of fair division. We present a polynomial-time algorithm that computes an allocation satisfying team-justified envy-freeness up to one participant, participant-justified envy-freeness, balancedness, Pareto optimality, and group-strategyproofness for participants, even in the possible presence of ties. Our algorithm generalizes both the Gale-Shapley algorithm from two-sided matching as well as the round-robin algorithm from fair division. We also discuss how our algorithm can be extended to accommodate quotas and incomplete preferences.

Problem

• Achieving two-sided fairness in many-to-one matching settings
• Generalizing Gale-Shapley and round-robin algorithms for fairness
• Ensuring fairness for both participants and teams with quotas

Innovation

• Generalizes Gale-Shapley and round-robin algorithms
• Satisfies multi-fairness criteria in polynomial time
• Extends to handle quotas and incomplete preferences