School choice with priority-based affirmative action: A responsive solution

Abstract

We propose a solution to the school choice problem with priority-based affirmative action. This solution is a special case of Kesten’s efficiency-adjusted deferred acceptance mechanism (henceforth, EADAM), specifically, we require that all minority students should give consent to priority waiving while none of the majority students consent. We formalize this solution as efficiency-adjusted deferred acceptance mechanism with only minorities consenting (henceforth, EADAMm). While it is known that when all students consent, the EADAM is not responsive to the priority-based affirmative action, we show that the EADAMm is responsive to the priority-based affirmative action. Inherited from the EADAM, the EADAMm satisfies reasonable fairness but lacks strategy-proofness. We further show that there is no reasonably fair and strategy-proof mechanism that is also responsive to the priority-based affirmative action.