Justifiable Priority Violations

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.