On Responsiveness of Two Competing Mechanisms to Affirmative Action in School Choice

Responsiveness to priority‐based affirmative action policy in school choice

“…It is natural to ask under what restrictions a mechanism can be strictly responsive to affirmative action policy. Jiao and Tian (2018), by considering the initial priorities and capacity vector, characterize the domain where sDA is responsive to affirmative action policy. They introduce an acyclicity condition which is the necessary and sufficient condition for sDA to be responsive to affirmative action policy.…”

“…For instance, when each school has one seat and there exist a majority student, $$s$$, and two minority students, $$s^{\prime} $$ and $$s^{\prime\prime} $$, and two schools, $$c$$ and $$c^{\prime} $$, such that $$s{\succ }_{c}s^{\prime} $$ and $$s{\succ }_{c^{\prime} }s^{\prime\prime} $$, then their acyclicity condition is violated. In fact, Jiao and Tian (2018) state in their paper that the result stating the necessary and sufficient condition for sDA to be responsive to affirmative action policy (Theorem 2) can be regarded as an impossibility result. Since strict responsiveness to affirmative action policy implies responsiveness to affirmative action policy, whenever their acyclicity condition is violated sDA fails to be strictly responsive to affirmative action policy.…”

“…In a recent paper, Jiao and Tian (2018) investigate the restrictions for sDA and TTC to be responsive to affirmative action policy. They show that sDA is responsive to affirmative action policy if and only if the initial priorities satisfy an acyclicity condition.…”

“…For instance, when schools have common priority order over the students, their acyclicity condition might fail. Since strict responsiveness to affirmative action is a stronger notion than the responsiveness to affirmative action policy, the restriction on the initial priority order to satisfy strict responsiveness to affirmative action policy will not be less demanding than the acyclicity condition of Jiao and Tian (2018). As a result, instead of investigating the restrictions on the initial priority order which guarantee strict responsiveness to affirmative action, we focus on setting restrictions on the priority improvements that can be made by the affirmative action policy.…”

“…Their results are counterparts of our results based on weak responsiveness to affirmative action policy under reserve‐based affirmative action policy. Jiao and Tian (2018) find that when all schools have the same priority orders over students, TTC is responsive to reserve‐based affirmative action policy while sDA is not.…”