Balancing Fairness and High Match Rates in Reciprocal Recommender Systems: A Nash Social Welfare Approach

2026-01-20

AI Summary

This work addresses the challenge of balancing matching efficiency and user fairness in two-sided recommendation systems by introducing, for the first time, the notion of envy-free fairness to define equitable allocation of recommendation opportunities. The authors propose an optimization approach based on Nash Social Welfare (NSW), design an alternating optimization mechanism, and generalize it into a tunable α-SW unified framework that flexibly trades off fairness against efficiency. To enable scalable computation, they employ the Sinkhorn algorithm to accelerate the approximate solution of the NSW objective. Experiments on synthetic and two real-world datasets demonstrate that the proposed method significantly improves fairness—approaching envy-free allocation—while maintaining high matching rates.

Technology Category

• Search and Optimization: Algorithm Configuration
• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Fair Division

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Economics and fairness of platforms and recommendation systems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Matching platforms, such as online dating services and job recommendations, have become increasingly prevalent. For the success of these platforms, it is crucial to design reciprocal recommender systems (RRSs) that not only increase the total number of matches but also avoid creating unfairness among users. In this paper, we investigate the fairness of RRSs on matching platforms. From the perspective of fair division, we define the users'opportunities to be recommended and establish the fairness concept of envy-freeness in the allocation of these opportunities. We first introduce the Social Welfare (SW) method, which approximately maximizes the number of matches, and show that it leads to significant unfairness in recommendation opportunities, illustrating the trade-off between fairness and match rates. To address this challenge, we propose the Nash Social Welfare (NSW) method, which alternately optimizes two NSW functions and achieves nearly envy-free recommendations. We further generalize the SW and NSW method to the $\alpha$-SW method, which balances the trade-off between fairness and high match rates. Additionally, we develop a computationally efficient approximation algorithm for the SW/NSW/$\alpha$-SW methods based on the Sinkhorn algorithm. Through extensive experiments on both synthetic datasets and two real-world datasets, we demonstrate the practical effectiveness of our approach.

Problem

• reciprocal recommender systems
• fairness
• match rates
• envy-freeness
• Nash Social Welfare

Innovation

• Nash Social Welfare
• Reciprocal Recommender Systems
• Envy-freeness
• Fairness-Match Trade-off
• Sinkhorn Algorithm