Responsiveness to priority-based affirmative action policy in school choice

We consider the priority-based affirmative action policy in school choice. We weaken the responsiveness to affirmative action policy by requiring at least one minority student to be weakly better off when their priorities are improved. We find that under both the student-proposing deferred acceptance mechanism and the top trading cycles mechanism at least one minority student becomes weakly better off when their priorities are improved. We also strengthen the responsiveness to affirmative action policy by requiring all minority students to be weakly better off when their priorities are improved. We call this property strict responsiveness to affirmative action policy. We find that there is no nonwasteful, individually rational, mutually best, and strategy-proof mechanism that is strictly responsive to affirmative action policy. We then find a sufficient condition for the affirmative action policy to satisfy for the student-proposing deferred acceptance mechanism to be strictly responsive to affirmative action policy by setting restrictions on the priority improvements made by the policy.