arXiv subjects

Tomohiko Yokoyama

Publications and source records attributed to Tomohiko Yokoyama.

5 recordsLinked to original sources

arXiv2026

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.

cs.IR↗

arXiv2025

Position Fair Mechanisms Allocating Indivisible Goods

Fair division mechanisms for indivisible goods require agent orderings to deterministically select one allocation when running the algorithm in practice. We introduce position envy-freeness up to one good (PEF1) as a fairness criterion for mechanisms: a mechanism is said to satisfy PEF1 if for any pair of agent orderings, no agent prefers their bundle determined under one ordering to that under another ordering by more than the utility of a single good. First, we propose a scale-invariant, polynomial-time mechanism that satisfies PEF1 and yields an envy-freeness up to one good (EF1) allocation. For the case of two agents, we establish that any mechanism producing a maximum Nash welfare allocation eliminates envy based on positions by removing one good, provided that utilities are positive. Additionally, we present a polynomial-time mechanism based on the adjusted winner procedure, which satisfies PEF1 and produces an EF1 and Pareto optimal allocation for two agents. In contrast, we demonstrate that well-known mechanisms such as round-robin and envy-cycle elimination do not generally satisfy PEF1.

cs.GT↗

arXiv2025

Asymptotic Analysis of Weighted Fair Division

Several resource allocation settings involve agents with unequal entitlements represented by weights. We analyze weighted fair division from an asymptotic perspective: if $m$ items are divided among $n$ agents whose utilities are independently sampled from a probability distribution, when is it likely that a fair allocation exist? We show that if the ratio between the weights is bounded, a weighted envy-free allocation exists with high probability provided that $m = Ω(n\log n/\log\log n)$, generalizing a prior unweighted result. For weighted proportionality, we establish a sharp threshold of $m = n/(1-μ)$ for the transition from non-existence to existence, where $μ\in (0,1)$ denotes the mean of the distribution. In addition, we prove that for two agents, a weighted envy-free (and weighted proportional) allocation is likely to exist if $m = ω(\sqrt{r})$, where $r$ denotes the ratio between the two weights.

cs.GT↗

arXiv2025

Asymptotic Existence of Class Envy-free Matchings

We consider a one-sided matching problem where agents who are partitioned into disjoint classes and each class must receive fair treatment in a desired matching. This model, proposed by Benabbou et al. [2019], aims to address various real-life scenarios, such as the allocation of public housing and medical resources across different ethnic, age, and other demographic groups. Our focus is on achieving class envy-free matchings, where each class receives a total utility at least as large as the maximum value of a matching they would achieve from the items matched to another class. While class envy-freeness for worst-case utilities is unattainable without leaving some valuable items unmatched, such extreme cases may rarely occur in practice. To analyze the existence of a class envy-free matching in practice, we study a distributional model where agents' utilities for items are drawn from a probability distribution. Our main result establishes the asymptotic existence of a desired matching, showing that a round-robin algorithm produces a class envy-free matching as the number of agents approaches infinity.

cs.GT↗

arXiv2025

Probabilistic Analysis of Stable Matching in Large Markets with Siblings

We study a practical centralized matching problem which assigns children to daycare centers. The collective preferences of siblings from the same family introduce complementarities, which can lead to the absence of stable matchings, as observed in the hospital-doctor matching problems involving couples. Intriguingly, stable matchings are consistently observed in real-world daycare markets, despite the prevalence of sibling applicants. We conduct a probabilistic analysis of large random markets to examine the existence of stable matchings in such markets. Specifically, we examine scenarios where daycare centers have similar priorities over children, a common characteristic in real-world markets. Our analysis reveals that as the market size approaches infinity, the likelihood of stable matchings existing converges to 1. To facilitate our exploration, we refine an existing heuristic algorithm to address a more rigorous stability concept, as the original one may fail to meet this criterion. Through extensive experiments on both real-world and synthetic datasets, we demonstrate the effectiveness of our revised algorithm in identifying stable matchings, particularly when daycare priorities exhibit high similarity.

cs.GT↗