In many settings, such as the rationing of medical care and supplies, university admissions, and the assignment of public housing, the decision of who receives an allocation can be justified by various normative criteria (ethical, financial, legal, etc.). These criteria can influence priorities and restrict the number of units available to particular demographics. We consider a setting wherein a set of identical items must be distributed among unit-demand applicants. The items are divided across a set of categories (each with an allocation quota), and each category has a priority ordering over its eligible applicants. Building on previous work, we define a set of natural desiderata for allocations. We use techniques from linear and integer programming to give a polynomial-time procedure for finding Pareto efficient allocations satisfying these desiderata. The clean formulation of our algorithm allows us to more easily derive known results in this space and provides the flexibility to consider alternate objectives and enforce various notions of equity between categories.
Fair and Efficient Allocation with Quotas