We examine a controlled school choice model in which students are divided into types and the distribution of admitted students influences schools’ priority structures. We introduce a general class of priority rules that represent priorities as weak orders (allowing ties) for each given assignment and satisfy three axioms: Preference for Diversity, Within-Type Ordering, and Distributional Consistency. This framework includes the adjusted scoring rule, which flexibly integrates reserves, quotas, and bonus-point rules while accounting for uncertainty in applicants’ types and scores. From such priority profiles, we construct choice functions that satisfy substitutability and size monotonicity. We show that the student-proposing deferred acceptance mechanism with these functions yields matchings that are stable with respect to the original priority profiles and satisfy group strategy-proofness. Moreover, when priority profiles are restricted to linear orders for each given assignment, our mechanism yields a student-optimal stable matching.
Kitahara et al. (Thu,) studied this question.