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

TL;DR

This work studies fairness in two-sided reciprocal recommender systems by formalizing envy-freeness of recommendation opportunities and connecting it to Pareto efficiency and Nash social welfare (NSW).It introduces SW (to maximize total matches), NSW (to balance fairness and efficiency), and α-SW (to interpolate between these objectives), along with a scalable Sinkhorn-based solver for large-scale problems.The NSW approach yields near-zero envy across both sides while maintaining competitive match rates, and the Sinkhorn extension significantly improves computation time with scalable performance on real and synthetic data.Empirical results across synthetic and real-world dating datasets (including a Japanese dating platform and speed dating data) demonstrate the practical benefits of NSW and α-SW for fair, efficient reciprocal recommendations.The work advances fair division concepts in RRSs and provides a flexible, scalable toolkit for balancing fairness with high match rates in two-sided matching platforms.

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 $α$-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/$α$-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.

Figures (9)

• Figure 1: Overview of the recommendation process in two-sided matching platforms. Agents on both sides receive probabilistic recommendation lists---represented by doubly stochastic matrices---and make application decisions based on estimated preference probabilities. A match is established when both agents mutually select each other.
• Figure 2: Expected number of matches.
• Figure 3: Envy for left-side agents.
• Figure 4: Envy for right-side agents.
• Figure 6: The four left figures show the Gini index of users' utilities (expected number of matches) in the synthetic data experiment for the case where $n = 75$, $m = 50$, $\lambda \in \{0.0,0.2,0.4,0.6,0.8,1.0\}$, and $e = \text{"log"}$ (a) or $e = \text{"inv"}$ (c). Mean value over 10 trials and 95% CI are reported. Four right figures are the utility distributions over all of 10 trials in the case of $n = 75$, $m = 50$, $\lambda = 0.8$, and $e = \text{"log"}$ (b) or $e = \text{"inv"}$ (d).

Theorems & Definitions (5)

• definition 1: Double envy-freeness
• definition 2: Pareto optimality
• proposition 1
• proposition 2
• theorem 1