Justifiable Priority Violations

2026-04-07

AI Summary

This study addresses the trade-off between inefficiency and priority violations inherent in the Deferred Acceptance (DA) mechanism by proposing an endogenous justifiability criterion: a priority violation is deemed acceptable if it directly benefits the affected student or if the student cannot benefit under any Pareto improvement over DA. This criterion obviates the need for ex ante individual consent, thereby overcoming limitations of existing frameworks. The authors design a “margin-admission” mechanism accompanied by a polynomial-time iterative algorithm that efficiently computes strongly justifiable matchings and expands the set of beneficiaries. Theoretical analysis establishes fundamental efficiency limits within both existing and proposed frameworks, while simulation results demonstrate that the new approach achieves Pareto improvements unattainable by current mechanisms.

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.

Problem

• priority violations
• Deferred Acceptance
• justifiability
• Pareto efficiency
• matching

Innovation

• endogenous justifiability
• priority violation
• Deferred Acceptance
• Pareto improvement
• matching mechanism