Post-Match Error Mitigation for Deferred Acceptance

TL;DR

This paper addresses errors in deferred-acceptance matching algorithms that occur after results are announced, proposing models and mitigation strategies tailored to different error scenarios to improve stability and fairness.

Contribution

It introduces new models for post-match errors and develops mitigation strategies specific to resource reduction, additive, and subtractive errors in DA algorithms.

Findings

Mitigation strategies can restore stability after errors.

Strategies vary based on administrator goals.

Empirical simulations demonstrate effectiveness.

Abstract

Real-life applications of deferred-acceptance (DA) matching algorithms sometimes exhibit errors or changes to the matching inputs that are discovered only after the algorithm has been run and the results are announced to participants. Mitigating the effects of these errors is a different problem than the original match since the decision makers are often constrained by the offers they already sent out. We propose models for this new problem, along with mitigation strategies to go with these models. We explore three different error scenarios: resource reduction, additive errors, and subtractive errors. For each error type, we compute the expected number of students directly harmed, or helped, by the error, the number indirectly harmed or helped, and the number of students with justified envy due to the errors. Error mitigation strategies need to be selected based on the goals of the administrator, which include restoring stability, avoiding direct harm to any participant, and focusing the extra burden on the schools that made the error. We provide empirical simulations of the errors and the mitigation strategies.