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Identifying and Quantifying (Un)Improvable Students

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Listed:
  • Josue Ortega
  • Gabriel Ziegler
  • R. Pablo Arribillaga
  • Geng Zhao

Abstract

The Deferred Acceptance (DA) mechanism can generate inefficient placements. Although Pareto-dominant mechanisms exist, it remains unclear which and how many students could improve. We characterize the set of unimprovable students and show that it includes those unassigned or matched with their least preferred schools. Nevertheless, by proving that DA's envy digraph contains a unique giant strongly connected component, we establish that almost all students are improvable, and furthermore, they can benefit simultaneously via disjoint trading cycles. Our findings reveal the pervasiveness of DA's inefficiency and the remarkable effectiveness of Pareto-dominant mechanisms in addressing it, regardless of the specific mechanism chosen.

Suggested Citation

  • Josue Ortega & Gabriel Ziegler & R. Pablo Arribillaga & Geng Zhao, 2024. "Identifying and Quantifying (Un)Improvable Students," Papers 2407.19831, arXiv.org, revised May 2025.
    • Handle: RePEc:arx:papers:2407.19831
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    References listed on IDEAS

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    1. Alfred Galichon & Octavia Ghelfi & Marc Henry, 2021. "Stable and extremely unequal," Papers 2108.06587, arXiv.org, revised Mar 2023.
    2. Galichon, Alfred & Ghelfi, Octavia & Henry, Marc, 2023. "Stable and extremely unequal," Economics Letters, Elsevier, vol. 226(C).
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