Overlapping Reserves without a Common Priority: Theory and an Application to School Choice in Chile

We study matching markets with overlapping reserves governed by heterogeneous priorities. When applicants qualify for multiple reserves, how they are routed can affect reserve utilization and which applicants are admitted. We introduce classify-and-rank choice rules that yield strategy-proof deferred acceptance mechanisms satisfying maximum reserve utilization and priority-respect. We axiomatically characterize our mechanism's admission outcomes for any given classification and reserve order. With two reserve categories, we provide a foundation for the reserve order and establish its distributional implications for access across eligibility groups. Using nine cycles of Chilean school admissions, which feature such reserves, we document reserve-utilization failures under the deployed mechanism and show that their frequency depends sharply on the reserve order. We show how our mechanism can be adapted to Chile's institutional setting to prevent such failures. Under this alternative mechanism, the reserve order generates a distributional pattern across eligibility groups, consistent with our theory.