Approximately Stable, School Optimal, and Student-Truthful Many-to-One Matchings (via Differential Privacy)

TL;DR

This paper introduces a differentially private algorithm for computing stable, school optimal matchings that incentivizes students to truthfully report their preferences, marking a novel advance in large market matching theory.

Contribution

It provides the first known method to ensure student truthfulness in school optimal matchings under worst-case preferences using differential privacy.

Findings

Achieves asymptotic stability and truthfulness guarantees

Uses differential privacy to coordinate matchings

Applicable to large markets with worst-case preferences

Abstract

We present a mechanism for computing asymptotically stable school optimal matchings, while guaranteeing that it is an asymptotic dominant strategy for every student to report their true preferences to the mechanism. Our main tool in this endeavor is differential privacy: we give an algorithm that coordinates a stable matching using differentially private signals, which lead to our truthfulness guarantee. This is the first setting in which it is known how to achieve nontrivial truthfulness guarantees for students when computing school optimal matchings, assuming worst- case preferences (for schools and students) in large markets.