Reserve Matching with Thresholds

Abstract: Reserve systems are used to accommodate multiple essential or underrepresented groups in allocating indivisible scarce resources by creating categories that prioritize their respective beneficiaries. Some applications include the optimal allocation of vaccines, or assignment of minority students to elite colleges in India. An allocation is called smart if it optimizes the number of units distributed. Previous literature mostly assumed baseline priorities, which impose significant interdependencies between the priority ordering of different categories. It also assumes either everybody is eligible for receiving a unit from any category, or only the beneficiaries are eligible. The comprehensive Threshold Model we propose allows independent priority orderings among categories and arbitrary beneficiary and eligibility thresholds, enabling policymakers to avoid comparing incomparables in affirmative action systems. We present a new smart reserve system that optimizes two objectives simultaneously to allocate scarce resources. Our Smart Pipeline Matching Mechanism achieves all desirable properties in the most general domain possible. Our results apply to any resource allocation market, but we focus our attention on the vaccine allocation problem.