How to control controlled school choice

We characterize choice rules for schools that regard students as substitutes, while at the same time expressing preferences for the diversity composition of the student body. The stable (or fair) assignment of students to schools requires the latter to regard the former as substitutes. Such a requirement is in conflict with the reality of schools’ preferences for a diverse student body. We show that the conflict can be useful, in the sense that certain unique rules emerge from imposing both considerations