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Fair Reciprocal Recommendation in Matching Markets

Yoji Tomita, Tomohiki Yokoyama

TL;DR

The paper tackles fairness in reciprocal recommender systems for two-sided matching by formalizing envy-freeness of recommendation opportunities and analyzing the trade-off with social welfare. It shows that socially optimal policies can induce substantial envy and introduces Nash Social Welfare-based methods to achieve approximately double envy-free outcomes, with theoretical guarantees under mild similarity assumptions. An alternating optimization framework is used to compute NSW-best policies, complemented by a practical heuristic based on maximum weight matchings. Empirical results on synthetic and real-world dating data demonstrate that NSW achieves near-zero envy while maintaining competitive match counts, highlighting its potential for fair and effective reciprocal recommendations in practice, albeit with scalability considerations for large-scale markets.

Abstract

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.

Fair Reciprocal Recommendation in Matching Markets

TL;DR

The paper tackles fairness in reciprocal recommender systems for two-sided matching by formalizing envy-freeness of recommendation opportunities and analyzing the trade-off with social welfare. It shows that socially optimal policies can induce substantial envy and introduces Nash Social Welfare-based methods to achieve approximately double envy-free outcomes, with theoretical guarantees under mild similarity assumptions. An alternating optimization framework is used to compute NSW-best policies, complemented by a practical heuristic based on maximum weight matchings. Empirical results on synthetic and real-world dating data demonstrate that NSW achieves near-zero envy while maintaining competitive match counts, highlighting its potential for fair and effective reciprocal recommendations in practice, albeit with scalability considerations for large-scale markets.

Abstract

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.
Paper Structure (23 sections, 1 theorem, 15 equations, 2 figures, 2 algorithms)

This paper contains 23 sections, 1 theorem, 15 equations, 2 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Reciprocal Recommender Systems (RRSs)
  4. Fair Reciprocal Recommendation
  5. Fair Division in Machine Learning
  6. Fair Division for Indivisible Goods
  7. Preliminaries
  8. Model
  9. Fairness Axioms
  10. Relationship to resource allocation problem
  11. Computing Socially Optimal Policy
  12. COMPUTING Fair Recommendation
  13. A heuristic method based on the matching problem
  14. Experiments
  15. Synthetic Data
  16. ...and 8 more sections

Key Result

theorem 1

For the case of $K=1$, if a policy induces NSW-best recommendations for both sides, then the policy is double envy-free. For the case of $K>1$, letting $\varepsilon$ be a non-negative constant, we assume that the estimated preference probabilities satisfies $\varepsilon$-similarity, and $n=\Theta(m)

Figures (2)

  • Figure 1: Results of experiments on synthetic data. Upper, middle and lower rows show the expected number of matches, the number of envies for left-side agents, and that for right-side agents for each case, respectively. We varies the number of left-side agents $n \in \{50, 75\}$, the examination functions $v = 1/\log_2(k+1)$ (log) or $1/k$ (inv), and lambda $\lambda \in \{0.0, 0.2, \dots, 1.0\}$, while we fixed the number of right-side agents $m = 50$, where each case correspond to each column. We conducted 10 experiments for each case, and report the mean of results and its 95% confidence intervals (but it is invisible in many cases due to its small variations.).
  • Figure 2: Results of experiments on the real-world data of a Japanese online dating platform. We conducted experiments $v(k) = 1/\log_2(k+1)$ (log) or $1/k$ (inv), and report the expected number of matches, the number of envy for male users and that of envy for female users.

Theorems & Definitions (2)

  • definition 1: Double envy-free policy
  • theorem 1