Controlled School Choice with Mixed Bounds Approach: A Balance Between Stability and Diversity Considerations

Controlled school choice over public schools has been an important concern for both the parents of students and schools. It gives numerous options for how fairness and diversity con- siderations can be balanced. The notion of diversity is often imposed by limiting the number of admitted students who have the same type (quotas), or by reserving seats for each student type (reserves). The controlled school choice rule that we explore in this paper is the combination of “reserves” and “quotas,” where schools implement minimum reserves (a “soft” bound) and maximum quotas (a “hard” bound) together. In this paper, we provide a full characterization of the mixed bounds approach, and show that it satisfies the requirements for the existence of a student-optimal stable matching.