Designing for Diversity: Matching with Slot-Specific Priorities

To encourage diversity, branches may vary contracts' priorities across slots. The agents who match to branches, however, have preferences only over match partners and contractual terms. Ad hoc approaches to resolving agents' indifferences across slots in the Chicago and Boston school choice programs have introduced biases, which can be corrected with more careful market design. Slot-specific priorities can fail the substitutability condition typically crucial for outcome stability. Nevertheless, an embedding into a one-to-one agent--slot matching market shows that stable outcomes exist and can be found by a cumulative offer mechanism that is strategy-proof and respects unambiguous improvements in priority.