Justifiable Priority Violations

TL;DR

This paper proposes a new, question-free method for justifying priority violations in the Deferred Acceptance mechanism, aiming to improve efficiency while maintaining fairness.

Contribution

It introduces an endogenous justifiability criterion and a polynomial-time algorithm to find strongly justifiable matchings, expanding on existing consent-based approaches.

Findings

The new mechanism always finds a strongly justifiable matching when DA is inefficient.

The algorithm iteratively improves matchings, converging to Pareto-efficient solutions.

Simulations show limitations of both consent-based and endogenous frameworks in practice.

Abstract

Addressing the large inefficiencies generated by the Deferred Acceptance (DA) mechanism requires priority violations, but which ones are justifiable? The leading approach is to ask individuals if they consent to waive their priority ex-ante. We develop an alternative question-free solution, in which a priority violation is justifiable whenever the affected student either (i) directly benefits from the improvement, or (ii) is unimprovable under any assignment that Pareto-dominates DA. This endogenous justifiability criterion permits improvements unattainable by the leading consent-based mechanism under any consent structure. We provide a ``just below cutoffs'' mechanism that always finds a strongly justifiable matching whenever DA's outcome is inefficient, and build on it to construct a polynomial-time algorithm that expands justifiable improvements iteratively, converging to a DA improvement that cannot be Pareto-improved by any justifiable matching without strictly expanding the beneficiary set. Finally, we prove theoretically that both the ex-ante consent and the endogenous justifiability frameworks have important limitations in reaching Pareto-efficient outcomes, and use simulations to quantify how binding these constraints are in practice.