Strategyproof Matching with Minimum Quotas

Abstract

We study matching markets in which institutions may have minimum and maximum quotas. Minimum quotas are important in many settings, such as hospital residency matching, military cadet matching, and school choice, but current mechanisms are unable to accommodate them, leading to the use of ad hoc solutions. We introduce two new classes of strategyproof mechanisms that allow for minimum quotas as an explicit input and show that our mechanisms improve welfare relative to existing approaches. Because minimum quotas cause a theoretical incompatibility between standard fairness and nonwastefulness properties, we introduce new second-best axioms and show that they are satisfied by our mechanisms. Last, we use simulations to quantify (1) the magnitude of the potential efficiency gains from our mechanisms and (2) how far the resulting assignments are from the first-best definitions of fairness and nonwastefulness. Combining both the theoretical and simulation results, we argue that our mechanisms will improve the performance of matching markets with minimum quota constraints in practice.

Controlled School Choice with Soft Bounds and Overlapping Types

“…Kamada and Kojima (2015) and consider regional maximum quotas. Biró et al (2010), Sönmez and Switzer (2013), Monte and Tumennasan (2013), , and Fragiadakis et al (2016) discuss how to handle minimum quotas. In the literature of computer science, the complexity of checking the existence of a stable matching has also been discussed when various distributional constraints are imposed (Huang, 2010;Fleiner & Kamiyama, 2016;Hamada, Iwama, & Miyazaki, 2016;Kamiyama, 2013).…”

“…In many application domains, various distributional constraints are often imposed on an outcome, e.g., regional maximum quotas are imposed on hospitals in urban areas so that more doctors are allocated to rural areas (Kamada & Kojima, 2015), or minimum quotas are imposed when school districts require that at least a certain number of students is allocated to each school so that the school can operate properly (Biró, Fleiner, Irving, & Manlove, 2010;Fragiadakis, Iwasaki, Troyan, Ueda, & Yokoo, 2016;Goto, Hashimoto, Iwasaki, Kawasaki, Ueda, Yasuda, & Yokoo, 2014). This paper deals with yet another type of distributional constraint, i.e., diversity constraints in school choice programs.…”

Towards a Fair Distribution Mechanism for Asylum

“…This strategy is not relevant here because the context of asylum is different to the setting where minimum quotas are usually investigated. For example, Fragiadakis, D., et al [30] investigate minimum quotas in the context of school choice. They assume that all schools are acceptable to all students and vice versa, and look at the case where the number of students is strictly between the sum of the schools' minimum quotas and the sum of the schools' maximum quotas.…”

“…In contrast, the problem we are concerned with is the case in which places may be wasted due to size of the set of acceptable refugee-country pairs. The special case where students may declare schools unacceptable is considered in [30], but their mechanisms allow violating minimum quotas and don't satisfy (MC).…”

Designing Matching Mechanisms under General Distributional Constraints

“…Public schools are often required to satisfy balance on the composition of students, typically in terms of socioeconomic status Ehlers, Hafalir, Yenmez, and Yildirim (2014). Several mechanisms have been proposed Ehlers, Hafalir, Yenmez, and Yildirim (2014); Fragiadakis, Iwasaki, Troyan, Ueda, and Yokoo (2015); Goto, Hashimoto, Iwasaki, Kawasaki, Ueda, Yasuda, and Yokoo (2014); ; Kamada and Kojima (2015) for each of these various constraints, but previous studies have focused on tailoring mechanisms to specific settings, rather than providing a general framework.…”