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Diversity in Choice as Majorization

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  • Federico Echenique
  • Teddy Mekonnen
  • M. Bumin Yenmez

Abstract

We use majorization to model comparative diversity in school choice. A population of agents is more diverse than another population of agents if its distribution over groups is less concentrated: being less concentrated takes a specific mathematical meaning borrowed from the theory of majorization. We adapt the standard notion of majorization in order to favor arbitrary distributional objectives, such as population-level distributions over race/ethnicity or socioeconomic status. With school admissions in mind, we axiomatically characterize choice rules that are consistent with modified majorization, and constitute a principled method for admitting a diverse population of students into a school. Two important advantages of our approach is that majorization provides a natural notion of diversity, and that our axioms are independent of any exogenous priority ordering. We compare our choice rule to the leading proposal in the literature, ``reserves and quotas,'' and find ours to be more flexible.

Suggested Citation

  • Federico Echenique & Teddy Mekonnen & M. Bumin Yenmez, 2024. "Diversity in Choice as Majorization," Papers 2407.17589, arXiv.org.
    • Handle: RePEc:arx:papers:2407.17589
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    References listed on IDEAS

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    1. Ehlers, Lars & Hafalir, Isa E. & Yenmez, M. Bumin & Yildirim, Muhammed A., 2014. "School choice with controlled choice constraints: Hard bounds versus soft bounds," Journal of Economic Theory, Elsevier, vol. 153(C), pages 648-683.
    2. Kojima, Fuhito, 2012. "School choice: Impossibilities for affirmative action," Games and Economic Behavior, Elsevier, vol. 75(2), pages 685-693.
    3. Arieli, Itai & Babichenko, Yakov & Smorodinsky, Rann & Yamashita, Takuro, 2023. "Optimal persuasion via bi-pooling," Theoretical Economics, Econometric Society, vol. 18(1), January.
    4. Andreas Kleiner & Benny Moldovanu & Philipp Strack, 2021. "Extreme Points and Majorization: Economic Applications," Econometrica, Econometric Society, vol. 89(4), pages 1557-1593, July.
    5. Yuichiro Kamada & Fuhito Kojima, 2015. "Efficient Matching under Distributional Constraints: Theory and Applications," American Economic Review, American Economic Association, vol. 105(1), pages 67-99, January.
    6. Atila Abdulkadiroğlu & Aram Grigoryan, 2021. "Priority-based Assignment with Reserves and Quotas," NBER Working Papers 28689, National Bureau of Economic Research, Inc.
    7. Isa E. Hafalir & Fuhito Kojima & M. Bumin Yenmez & Koji Yokote, 2022. "Design on Matroids: Diversity vs. Meritocracy," Papers 2301.00237, arXiv.org.
    8. Federico Echenique & M. Bumin Yenmez, 2015. "How to Control Controlled School Choice," American Economic Review, American Economic Association, vol. 105(8), pages 2679-2694, August.
    9. Aygün, Orhan & Turhan, Bertan, 2023. "Affirmative Action in India: Restricted Strategy Space, Complex Constraints, and Direct Mechanism Design," ISU General Staff Papers 202310041552400000, Iowa State University, Department of Economics.
    10. , Emin & , Bumin & , Ali, 2013. "Effective affirmative action in school choice," Theoretical Economics, Econometric Society, vol. 8(2), May.
    11. David Delacrétaz & Scott Duke Kominers & Alexander Teytelboym, 2023. "Matching Mechanisms for Refugee Resettlement," American Economic Review, American Economic Association, vol. 113(10), pages 2689-2717, October.
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