Justifiable Priority Violations
This addresses inefficiencies in school choice or matching systems for policymakers and economists, offering a novel alternative to consent-based mechanisms.
The paper tackles inefficiencies in the Deferred Acceptance (DA) mechanism by introducing an endogenous justifiability criterion for priority violations, which allows improvements unattainable by consent-based methods and provides a polynomial-time algorithm to find such matchings. It also theoretically and empirically shows limitations of both approaches in achieving Pareto efficiency.
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.