Fair Stable Matching Meets Correlated Preferences

TL;DR

This paper investigates the fairness of stable matchings under correlated preferences, showing empirically that the Deferred Acceptance algorithm often yields fair solutions with low sex-equality cost in practical scenarios.

Contribution

It provides empirical analysis of sex-equal stable matchings under correlated preferences, highlighting the practical fairness of the Deferred Acceptance algorithm.

Findings

DA algorithm produces low sex-equality cost under correlated preferences

Correlated preferences improve the fairness of stable matchings

Empirical evidence supports DA's broad practical use

Abstract

The stable matching problem sets the economic foundation of several practical applications ranging from school choice and medical residency to ridesharing and refugee placement. It is concerned with finding a matching between two disjoint sets of agents wherein no pair of agents prefer each other to their matched partners. The Deferred Acceptance (DA) algorithm is an elegant procedure that guarantees a stable matching for any input; however, its outcome may be unfair as it always favors one side by returning a matching that is optimal for one side (say men) and pessimal for the other side (say women). A desirable fairness notion is minimizing the sex-equality cost, i.e. the difference between the total rankings of both sides. Computing such stable matchings is a strongly NP-hard problem, which raises the question of what tractable algorithms to adopt in practice. We conduct a series of empirical evaluations on the properties of sex-equal stable matchings when preferences of agents on both sides are correlated. Our empirical results suggest that under correlated preferences, the DA algorithm returns stable matchings with low sex-equality cost, which further confirms its broad use in many practical applications.