Processing Reserves Simultaneously

Abstract

Policymakers frequently use reserve categories to combine competing objectives in allocating scarce resources based on priority. For example, schools may prioritize students from underprivileged backgrounds for some of their seats while allocating the rest of them based solely on academic merit. The order in which different categories are processed has been shown to have an important, yet subtle impact on allocative outcomes-and has led to unintended consequences in practice. I introduce a new, more transparent way of processing reserves, which handles all categories simultaneously. I provide an axiomatic characterization of my solution, showing that it satisfies basic desiderata as well as category neutrality: if an agent qualifies for n categories, she takes 1/n units from each of them. A practical advantage of this approach is that the relative importance of categories is entirely captured by their quotas.

Allocating with Priorities and Quotas: Algorithms, Complexity, and Dynamics

“…While [PE] is clearly a desirable property, it is a stronger efficiency requirement than those considered in prior work; in particular, it implies the "non-wastefulness" axiom used in (Pathak et al, 2021;Delacrétaz, 2021;Aziz and Brandl, 2021). Although the "maximum size matching" property of Aziz and Brandl (2021) appears to be stronger than Pareto efficiency, we argue that they are in fact equivalent in Section 3.1.…”

“…As mentioned, we build on the recent work of Pathak et al (2021), which has also inspired several other follow-up papers, with two of particular note. On the question of allocation selection, Delacrétaz (2021) notes that the policy of Pathak et al (2021) is not uniquely specified, and different choices can induce biases in the allocation. He then attempts to allay this concern by introducing a waterfilling-style simultaneous allocation procedure that leads to a unique (fractional) outcome.…”

“…A natural question now, given the above setting, is which properties make an allocation "satisfactory." The following two desiderata were proposed as axioms by Pathak et al ( 2021) (and adopted by Delacrétaz (2021) and Aziz and Brandl (2021)) as a natural formalism implied by the agent eligibility and priorities. We inherit the statements for fractional matchings from Delacrétaz, as these naturally generalize their integral counterparts.…”

“…Another axiom states that no category's allocation exceeds its quota. (This is either explicitly stated or implied in (Pathak et al, 2021;Delacrétaz, 2021;Aziz and Brandl, 2021). )…”

“…The third axiom ensures that priorities are respected, by requiring that a category never allocate to an agent if a higher-priority agent does not have full allocation; this is a trickier requirement, in particular, when combined with partial eligibility lists. Indeed, past work on this problem (Pathak et al, 2021;Delacrétaz, 2021) eschews finding Pareto efficient allocations, and while Aziz and Brandl (2021) provide a scheme to find a maximal (and hence Pareto efficient) allocation, they do not give any insight into the structure of satisfactory allocations, or how one can select from them to improve any secondary performance measure such as equity of allocations.…”