School choice under partial fairness

Abstract

We generalize the school choice problem by defining a notion of allowable priority violations. In this setting, a weak axiom of stability (partial stability) allows only certain priority violations. We introduce a class of algorithms called the student exchange under partial fairness (SEPF). Each member of this class gives a partially stable matching that is not Pareto dominated by another partially stable matching (i.e., constrained efficient in the class of partially stable matchings). Moreover, any constrained efficient matching that Pareto improves upon a partially stable matching can be obtained via an algorithm within the SEPF class. We characterize the unique algorithm in the SEPF class that satisfies a desirable incentive property. The extension of the model to an environment with weak priorities enables us to provide a characterization result that proves the counterpart of the main result in Erdil and Ergin (2008).

Essentially stable matchings

“…Finally, we show that essential stability is independent of the no-consent-proofness property of Dur et al (2015) by constructing two mechanisms, each of which satisfies exactly one of the two properties. First, the following mechanism is no-consent-proof, but not essentially stable: Ask everyone if they are willing to consent to having all of their priorities violated.…”

“…The goal is then to use a mechanism that ensures students cannot gain from not consenting, or in other words the mechanism should be no-consent-proof. This is the original approach taken in Kesten's (2010) paper introducing the EADA mechanism, and was further expanded by Dur et al (2015), who show that EADA is the unique constrained efficient mechanism that Pareto dominates DA and is no-consent-proof. 5 While related, there is an important conceptual distinction between the approaches.…”

Blocking Pairs Versus Blocking Students: Stability Comparisons in School Choice

“…Step 2: By Lemma 6 of Dur et al (2019), for any Pareto improvement µ over the DA assignment µ, there exist a set of disjoint improvement cycles (that is, no two improvement cycles share a common student) such that µ can be obtained from µ by implementing the improvement cycles. Since any two improvement cycles are disjoint, there is a unique efficient Pareto improvement over the DA assignment.…”

“…6 See Section 4 for a definition of an improvement cycle 7 Dogan and Yenmez (2020), Dur et al (2019), Ehlers and Morrill (2020), Kwon and Shorrer (2019), Tang and Zhang (2020), and Troyan et al (2020) provide different other justifications for EADA. school choice mechanisms are compared in terms of their manipulability by comparing the sets of problems, in the set inclusion sense, at which they are manipulable.…”

Consistent Pareto improvement over the student-optimal stable mechanism

“…Recently, EADAM has received attention in the literature (Dur et al 2019;Troyan et al 2018;Tang and Zhang 2017;Ehlers and Morrill 2017). These papers weaken stability and provide a different justification of EADAM.…”