Justified-envy Minimal Mechanisms in School Choice

Kwon, Hyuk‐Jun; Shorrer, Ran I.

doi:10.2139/ssrn.3495266

Cited by 9 publications

(26 citation statements)

References 39 publications

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“…Furthermore, if ψ is f -minimally unstable among efficient and strategyproof mechanisms, then ψ is weakly fminimally unstable among efficiency and strategyproof mechanisms (but the converse does not hold as there might exist a mechanism different from ψ with the identical f -stability measure). Abdulkadiroglu et al (2019) and Kwon and Shorrer (2019) use the weaker second definition and impose in addition comparability (among mechanisms) for their partial relations.…”

Section: A Unifying Approach To Stability Comparisonsmentioning

confidence: 99%

“…A natural alternative is to count the number of blocking pairs, which induces a complete comparison method (as all assignments can be compared by counting blocking pairs) and it is not immediate from Abdulkadiroglu et al (2019) whether TTC is minimally unstable among efficient and strategyproof mechanisms also based on this alternative cardinal comparison method. One may also consider comparison methods that are not based on the set of blocking pairs, but based on alternative sets such as (i) the set of blocking triplets 2 as in Kwon and Shorrer (2019) 3 or (ii) the set of blocking students 4 as in Dogan and Ehlers (2020). 5 Possibly, TTC is minimally unstable among efficient and strategyproof mechanisms for certain comparison methods but not for others.…”

Section: Introductionmentioning

confidence: 99%

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Robust Minimal Instability of the Top Trading Cycles Mechanism

Doğan

Ehlers

2020

SSRN Journal

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In the context of priority-based resource allocation, we formulate methods to compare assignments in terms of their stability as binary relations (on the set of possible assignments) that depend on the preference and the priority profile. We introduce three basic properties, stability preferred, separability, and consistency, that a reasonable stability comparison should satisfy. We show that, for any stability comparison satisfying the three properties, the top trading cycles (TTC) mechanism is minimally unstable among efficient and strategy-proof mechanisms in one-to-one matching. An important consequence is the robustness of a recent result by Abdulkadiroglu et al. (2019), which uses a particular stability comparison method where an assignment is more stable than another assignment if the set of blocking pairs in the former assignment is a subset of the set of blocking pairs in the latter assignment. Our unifying approach covers basically all natural comparison methods and it includes many cardinal stability comparison methods as special cases. * Battal Dogan acknowledges financial support from the British Academy/Leverhulme Trust (SRG1819\190133). Lars Ehlers acknowledges financial support from the SSHRC (Canada) and the FRQSC (Québec). We thank participants at several seminars and conferences for valuable comments and suggestions.

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Section: A Unifying Approach To Stability Comparisonsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust Minimal Instability of the Top Trading Cycles Mechanism

Doğan

Ehlers

2020

SSRN Journal

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“…The closest studies to ours are Abdulkadiroglu et al (2020), 8 Kwon and Shorrer (2019), and Tang and Zhang (2020), which also compare school choice mechanisms, and assignments, in terms of their stability. Although these studies also consider minimally unstable assignments, to our knowledge, our study is the first to consider cardinally minimally unstable assignments in school choice.…”

Section: Introductionmentioning

confidence: 97%

“…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.…”

Section: Introductionmentioning

confidence: 99%

“…This result also implies that the EADA mechanism is minimally unstable among efficient assignments. Kwon and Shorrer (2019) introduce the notion of a blocking triplet which includes, in addition to a blocking pair, a student who violates the priority of the student in the blocking pair. Kwon and Shorrer (2019) show that the EADA mechanism is minimally unstable among efficient assignments also when stability comparison is based on comparing (in the set-inclusion sense) sets of blocking triplets.…”

Section: Introductionmentioning

confidence: 99%

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Blocking Pairs Versus Blocking Students: Stability Comparisons in School Choice

Doğan

Ehlers

2020

SSRN Journal

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It is known that there are school choice problems without an efficient and stable assignment. We consider comparing assignments in terms of their stability by comparing their sets of blocking (student-school) pairs or comparing their sets of blocking students who are involved in at least one blocking pair. Although there always exists a Pareto improvement over the student-optimal stable (DA) assignment which is minimally unstable among efficient assignments when the stability comparison is based on comparing the sets of blocking pairs in the set-inclusion sense, we show that this is not necessarily true when the stability comparison is based on comparing the sets of blocking pairs in the cardinal sense, or when it is based on comparing sets of blocking students (in the set-inclusion or cardinal sense). Given the latter impossibilities, we characterize the priority profiles where there exists a Pareto improvement over the DA mechanism which is cardinally minimally stable among efficient assignments when counting blocking pairs or counting blocking students. The resulting domain restrictions suggest to take with caution school choice analysis which relies on a particular stability comparison method.

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Rawlsian Matching

Afacan,

Dur

2024

Mathematical Social Sciences

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Justified-envy Minimal Mechanisms in School Choice

Cited by 9 publications

References 39 publications

Robust Minimal Instability of the Top Trading Cycles Mechanism

Robust Minimal Instability of the Top Trading Cycles Mechanism

Blocking Pairs Versus Blocking Students: Stability Comparisons in School Choice

Rawlsian Matching

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