Unified versus divided enrollment in school choice: Improving student welfare in Chicago

The Chicago Board of Education is implementing a centralized clearinghouse to assign students to schools since 2018-19 admissions. In this clearinghouse, each student can simultaneously be admitted to a selective and a nonselective school. We study this divided enrollment system and show that an alternative unified enrollment system, which elicits the preferences of students over all schools and assigns each student to only one school, is better for students when choice rules of schools are substitutable. If the choice rule of a school is not substitutable, then there exist student preferences such that at least one student strictly prefers the divided enrollment system to the unified enrollment system. Furthermore, we characterize the sources of inefficiency in the divided enrollment system when choice rules of schools are substitutable.