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Social Choice and Welfare

Erschienen in:

27.07.2022 | Original Paper

Top trading cycles with reordering: improving match priority in school choice

verfasst von: Aram Grigoryan

Erschienen in: Social Choice and Welfare | Ausgabe 3/2023

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Abstract

School districts commonly ration public school seats based on students’ preferences and schools’ priorities. Priorities reflect the school districts’ objectives for reducing busing costs (walk-zone priority) or utilizing siblings’ learning spillovers (sibling priority). I develop a simple modification of the well-studied Top Trading Cycles mechanism that matches schools to higher priority students while preserving the mechanism’s desirable efficiency and incentives properties.

Vorheriger Artikel The theory of straight ticket voting

Nächster Artikel Robust dissimilarity comparisons with categorical outcomes

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The assumptions that there are equal number of students and school seats and that all schools are acceptable is without loss of generality; we can introduce additional schools that represent being unassigned, and additional students who prefer to be unassigned and the arguments would carry through.

Hatfield et al. (2016) prove the result in their Supplementary Appendix (Proposition 9). The intuition behind the result is that when a student’s priority rank is reduced (improved), she is pointed by less (more) schools, either directly or indirectly. Hence, she can ‘afford’ less (more) schools under the TTC after the reduction (improvement).

Since the average number of justified-envy instances is the same under TTC and TTC-R, the two mechanisms are also not comparable with respect to the justified-envy comparison notion in Abdulkadiroğlu et al. (2020).

I thank an anonymous reviewer for highlighting this shortcoming of TTC-R.

For the sake brevity, a transposition is given only by mentioning which elements are swapped.

Abdulkadiroğlu A, Sönmez T (2003) School choice: a mechanism design approach. Am Econ Rev 93:729–747CrossRef

Abdulkadiroğlu A, Che Y-K, Pathak P, Roth A, Tercieux O (2020) Efficiency, justified envy, and incentives in priority-based matching. Am Econ Rev Insights

Abdulkadiroğlu A, Dur U, Grigoryan A (2021) School choice with match quality. National Bureau of Economic Research, Working Paper No 28512

Balinski M, Sönmez T (1999) A tale of two mechanisms: student placement. J Econ Theory 84:73–94CrossRef

Che Y-K, Tercieux O (2017) Top trading cycles in prioritized matching: an irrelevance of priorities in large markets. Manuscript. Columbia Univ. and Paris School Econ

Dur U, Kominers SD, Pathak PA, Sönmez T (2018) Reserve design: unintended consequences and the demise of Boston’s walk zones. J Polit Econ 6:2457–2479CrossRef

Dur U, Morrill T, Phan W (2021) Family ties: school assignment with siblings. Theor Econ

Gale D, Shapley LS (1962) College admissions and the stability of marriage. Am Math Mon 69:9–15CrossRef

Hakimov R, Kesten O (2018) The equitable top trading cycles mechanism for school choice. Int Econ Rev 59:2219–2258CrossRef

Hatfield JW, Kojima F, Narita Y (2016) Improving schools through school choice: a market design approach. J Econ Theory 166:186–211CrossRef

Menino T (2012) Recommendation to implement a new BPS assignment algorithm, State of the City, January 17. http://www.cityofboston.gov/

Morrill T (2015) Two simple variations of top trading cycles. Econ Theor 60:123–140CrossRef

Shapley L, Scarf H (1974) On cores and indivisibility. J Math Econ 1:23–28CrossRef

Shi P (2021) Optimal priority-based allocation mechanisms. Manag Sci

Titel: Top trading cycles with reordering: improving match priority in school choice
verfasst von: Aram Grigoryan
Publikationsdatum: 27.07.2022
Verlag: Springer Berlin Heidelberg
Erschienen in: Social Choice and Welfare / Ausgabe 3/2023
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-022-01422-6

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