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Diversity as Majorization

Author

Listed:
  • Federico Echenique
  • Teddy Mekonnen
  • M. Bumin Yenmez

Abstract

How should institutions compare group diversity, and which group should they select when they value diversity and merit? We take a target-based approach that evaluates the entire group composition without treating any type as intrinsically diversity-enhancing. Because different diversity indices may rank groups differently, we instead adapt majorization to construct an ordinal diversity preorder. We show that its maximally diverse selections are exactly those maximizing every index in a broad class. This characterization yields a reserve-and-quota policy that selects a maximally diverse group and, among such groups, the highest-merit agents. Any alternative is less diverse, less meritorious, or both.

Suggested Citation

  • Federico Echenique & Teddy Mekonnen & M. Bumin Yenmez, 2026. "Diversity as Majorization," Papers 2608.11497, arXiv.org.
    • Handle: RePEc:arx:papers:2608.11497
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    References listed on IDEAS

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    1. Fuhito Kojima, 2012. "The “rural hospital theorem” revisited," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(1), pages 67-76, March.
    2. Aygün, Orhan & Turhan, Bertan, 2020. "Dynamic reserves in matching markets," Journal of Economic Theory, Elsevier, vol. 188(C).
    3. Friedrich Pukelsheim, 2017. "Proportional Representation," Springer Books, Springer, edition 2, number 978-3-319-64707-4, December.
    4. Fragiadakis, Daniel & Troyan, Peter, 2017. "Improving matching under hard distributional constraints," Theoretical Economics, Econometric Society, vol. 12(2), May.
    5. Federico Echenique & Teddy Mekonnen & M. Bumin Yenmez, 2026. "Distributional Preferences for Market Design," Papers 2602.08035, arXiv.org, revised Aug 2026.
    6. Alexander Westkamp, 2013. "An analysis of the German university admissions system," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(3), pages 561-589, August.
    7. 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.
    8. Imamura, Kenzo, 2025. "Meritocracy versus diversity," Journal of Economic Theory, Elsevier, vol. 228(C).
    9. , Emin & , Bumin & , Ali, 2013. "Effective affirmative action in school choice," Theoretical Economics, Econometric Society, vol. 8(2), May.
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