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

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.

Fair Reciprocal Recommendation in Matching Markets

Recommender systems play an increasingly crucial role in shaping people's opportunities, particularly in online dating platforms. It is essential from the user's perspective to increase the probability of matching with a suitable partner while ensuring an appropriate level of fairness in the matching opportunities. We investigate reciprocal recommendation in two-sided matching markets between agents divided into two sides. In our model, a match is considered successful only when both individuals express interest in each other. Additionally, we assume that agents prefer to appear prominently in the recommendation lists presented to those on the other side. We define each agent's opportunity to be recommended and introduce its fairness criterion, envy-freeness, from the perspective of fair division theory. The recommendations that approximately maximize the expected number of matches, empirically obtained by heuristic algorithms, are likely to result in significant unfairness of opportunity. Therefore, there can be a trade-off between maximizing the expected matches and ensuring fairness of opportunity. To address this challenge, we propose a method to find a policy that is close to being envy-free by leveraging the Nash social welfare function. Experiments on synthetic and real-world datasets demonstrate the effectiveness of our approach in achieving both relatively high expected matches and fairness for opportunities of both sides in reciprocal recommender systems.

Fast and Examination-agnostic Reciprocal Recommendation in Matching Markets

In matching markets such as job posting and online dating platforms, the recommender system plays a critical role in the success of the platform. Unlike standard recommender systems that suggest items to users, reciprocal recommender systems (RRSs) that suggest other users must take into account the mutual interests of users. In addition, ensuring that recommendation opportunities do not disproportionately favor popular users is essential for the total number of matches and for fairness among users. Existing recommendation methods in matching markets, however, face computational challenges on large-scale platforms and depend on specific examination functions in the position-based model (PBM). In this paper, we introduce the reciprocal recommendation method based on the matching with transferable utility (TU matching) model in the context of ranking recommendations in matching markets and propose a fast and examination-model-free algorithm. Furthermore, we evaluate our approach on experiments with synthetic data and real-world data from an online dating platform in Japan. Our method performs better than or as well as existing methods in terms of the total number of matches and works well even in a large-scale dataset for which one existing method does not work.

Matching Theory-based Recommender Systems in Online Dating

Online dating platforms provide people with the opportunity to find a partner. Recommender systems in online dating platforms suggest one side of users to the other side of users. We discuss the potential interactions between reciprocal recommender systems (RRSs) and matching theory. We present our ongoing project to deploy a matching theory-based recommender system (MTRS) in a real-world online dating platform.