Responsive Affirmative Action in School Choice

School choice programs aim to give students the option to choose their school. At the same time, underrepresented minority students should be favored to close the opportunity gap. A common way to achieve this is to have a majority quota at each school, and to require that no school be assigned more majority students than its majority quota. An alternative way is to reserve some seats at each school for the minority students, and to require that a reserve seat at a school be assigned to a majority student only if no minority student prefers that school to her assignment. However, fair rules based on either type of affirmative action suffer from a common problem: a stronger affirmative action may not benefit any minority student and hurt some minority students. First, we show that this problem is pervasive: the problem disappears only if the minority students "mostly" have priority over the majority students. Then, we uncover the root of this problem: for some minority students, treating them as minority students does not benefit them, but possibly hurts other minority students. We propose a new assignment rule (Modified deferred acceptance with minority reserves), which treats such minority students as majority students, achieves affirmative action, and never hurts a minority student without benefiting another minority student.