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Blocking Pairs versus Blocking Students: Stability Comparisons in School Choice

Battal Dogan and Lars Ehlers

No 04-2020, Cahiers de recherche from Centre interuniversitaire de recherche en économie quantitative, CIREQ

Abstract: 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.

Keywords: school choice; stability comparisons; minimal instability; deferred acceptance (search for similar items in EconPapers)
JEL-codes: C70 D47 D61 D63 (search for similar items in EconPapers)
Date: 2020-04
New Economics Papers: this item is included in nep-des and nep-ure
References: Add references at CitEc
Citations: View citations in EconPapers (1)

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