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Weighted school choice problems and the weighted top trading cycles mechanism

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  • Stroh-Maraun, Nadja

Abstract

There are a number of school choice problems in which students are heterogeneous according to the number of seats they occupy at the school they are assigned to. We propose a weighted school choice problem by assigning each student a so-called weight and formulate the weighted top trading cycles algorithm (WTTC) to find a matching. The WTTC is strategy-proof and results in a Pareto efficient matching. While the WTTC is a robust extension of the TTC when weights are introduced, it is no longer guaranteed that each student gets a seat at a school even if the overall capacity exceeds the sum of weights. Additionally, the WTTC introduces a trade-off between weights and priorities as a student with a higher weight has a disadvantage to be matched to a particular school compared to a student with the same schools’ priorities but a smaller weight.

Suggested Citation

  • Stroh-Maraun, Nadja, 2024. "Weighted school choice problems and the weighted top trading cycles mechanism," Mathematical Social Sciences, Elsevier, vol. 132(C), pages 49-56.
    • Handle: RePEc:eee:matsoc:v:132:y:2024:i:c:p:49-56
    DOI: 10.1016/j.mathsocsci.2024.09.001
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    More about this item

    Keywords

    Matching; School choice; College admission problems; Top trading cycles; Pareto efficiency; Strategy-proofness;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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