When Is the Deferred Acceptance Mechanism Responsive to Priority-based Affirmative Action?

For school choice problems with affirmative action, responsiveness is used as a measure of how a matching mechanism performs in terms of a certain type of affirmative action policy. We know that the Deferred Acceptance (DA) mechanism is not responsive to the priority-based affirmative action on the universal domain of school choice. As a further study, we show in this paper that, the DA mechanism is responsive to the priority-based affirmative action if and only if the schools' priority structure satisfies an acyclicity condition characterized in this paper. This acyclicity condition is stronger than Doğan's acyclicity, which is the necessary and sufficient condition for the DA mechanism to be responsive to the reserved-based affirmative action