The Dichotomous Affiliate Stable Matching Problem: Approval-Based Matching with Applicant-Employer Relations

TL;DR

This paper introduces the Dichotomous Affiliate Stable Matching (DASM) problem, modeling complex applicant-employer relationships with approval-based preferences, and provides an efficient algorithm with proven stability and empirical validation.

Contribution

The paper formulates the DASM problem with approval preferences, proves the existence of stable matchings, and develops an efficient algorithm validated through experiments and a human study.

Findings

Real-world preferences follow the valuation model

Stable solutions always exist under the model

Proposed algorithm outperforms linear programming approaches

Abstract

While the stable marriage problem and its variants model a vast range of matching markets, they fail to capture complex agent relationships, such as the affiliation of applicants and employers in an interview marketplace. To model this problem, the existing literature on matching with externalities permits agents to provide complete and total rankings over matchings based off of both their own and their affiliates' matches. This complete ordering restriction is unrealistic, and further the model may have an empty core. To address this, we introduce the Dichotomous Affiliate Stable Matching (DASM) Problem, where agents' preferences indicate dichotomous acceptance or rejection of another agent in the marketplace, both for themselves and their affiliates. We also assume the agent's preferences over entire matchings are determined by a general weighted valuation function of their (and their affiliates') matches. Our results are threefold: (1) we use a human study to show that real-world matching rankings follow our assumed valuation function; (2) we prove that there always exists a stable solution by providing an efficient, easily-implementable algorithm that finds such a solution; and (3) we experimentally validate the efficiency of our algorithm versus a linear-programming-based approach.