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Improving Community Cohesion in School Choice via Correlated-Lottery Implementation

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  • Itai Ashlagi

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Peng Shi

    (Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

In school choice, children submit a preference ranking over schools to a centralized assignment algorithm, which takes into account schools’ priorities over children and uses randomization to break ties. One criticism of existing school choice mechanisms is that they tend to disperse communities, so children do not go to school with others from their neighborhood. We suggest improving community cohesion by implementing a correlated lottery in a given school choice mechanism: we find a convex combination of deterministic assignments that maintains the original assignment probabilities, thus maintaining choice but improving community cohesion. To analyze the gain in cohesion for a wide class of mechanisms, we first prove the following characterization, which may be of independent interest: any mechanism that, in the large market limit, is nonatomic, Bayesian incentive compatible, symmetric, and efficient within each priority class is a “lottery-plus-cutoff” mechanism. This means that the large market limit can be described as follows: given the distribution of preferences, every student receives an identically distributed lottery number, every school sets a lottery cutoff for each priority class, and a student is assigned to her most preferred school for which she meets the cutoff. This generalizes liu-pycia-2012 to allow arbitrary priorities. Using this, we derive analytic expressions for maximum cohesion under a large market approximation. We show that the benefit of lottery-correlation is greater when students’ preferences are more correlated. In practice, although the correlated-lottery implementation problem is NP-hard, we present a heuristic that does well. We apply this to real data from Boston elementary school choice 2012 and find that we can increase cohesion by 79% for kindergarten 1 (K1) and 37% for kindergarten 2 (K2) new families. Greater cohesion gain is possible (tripling cohesion for K1 and doubling for K2) if we reduce the choice menus on top of applying lottery correlation.

Suggested Citation

  • Itai Ashlagi & Peng Shi, 2014. "Improving Community Cohesion in School Choice via Correlated-Lottery Implementation," Operations Research, INFORMS, vol. 62(6), pages 1247-1264, December.
    • Handle: RePEc:inm:oropre:v:62:y:2014:i:6:p:1247-1264
    DOI: 10.1287/opre.2014.1319
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    Cited by:

    1. Dur, Umut Mert & Wiseman, Thomas, 2019. "School choice with neighbors," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 101-109.
    2. Peng Shi, 2015. "Guiding School-Choice Reform through Novel Applications of Operations Research," Interfaces, INFORMS, vol. 45(2), pages 117-132, April.
    3. Marco Chiarandini & Rolf Fagerberg & Stefano Gualandi, 2019. "Handling preferences in student-project allocation," Annals of Operations Research, Springer, vol. 275(1), pages 39-78, April.
    4. Afacan, Mustafa Oǧuz, 2018. "The object allocation problem with random priorities," Games and Economic Behavior, Elsevier, vol. 110(C), pages 71-89.
    5. Peng Shi, 2022. "Optimal Priority-Based Allocation Mechanisms," Management Science, INFORMS, vol. 68(1), pages 171-188, January.
    6. Perach, Nitsan & Anily, Shoshana, 2022. "Stable matching of student-groups to dormitories," European Journal of Operational Research, Elsevier, vol. 302(1), pages 50-61.
    7. Itai Feigenbaum & Yash Kanoria & Irene Lo & Jay Sethuraman, 2020. "Dynamic Matching in School Choice: Efficient Seat Reassignment After Late Cancellations," Management Science, INFORMS, vol. 66(11), pages 5341-5361, November.
    8. Will Ma, 2023. "When Is Assortment Optimization Optimal?," Management Science, INFORMS, vol. 69(4), pages 2088-2105, April.
    9. Allman, Maxwell & Ashlagi, Itai & Nikzad, Afshin, 2023. "On rank dominance of tie-breaking rules," Theoretical Economics, Econometric Society, vol. 18(2), May.
    10. Itai Ashlagi & Peng Shi, 2016. "Optimal Allocation Without Money: An Engineering Approach," Management Science, INFORMS, vol. 62(4), pages 1078-1097, April.
    11. Ashlagi, Itai & Nikzad, Afshin & Romm, Assaf, 2019. "Assigning more students to their top choices: A comparison of tie-breaking rules," Games and Economic Behavior, Elsevier, vol. 115(C), pages 167-187.

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