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Desirability and social ranking

Author

Listed:
  • Michele Aleandri

    (LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma])

  • Felix Fritz

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Stefano Moretti

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

We present an axiomatic study of various solutions to the social ranking problem, where a solution links any ranking of coalitions of players to a binary relation between individual players. We focus on solutions that align with the desirability relation, asserting that player i is more desirable than player j if any coalition including i but not j ranks higher than the corresponding coalition formed by replacing i with j. Unlike previous characterizations, our study highlights the central role of the desirability property as a foundational axiom in the characterization of five solutions from the related literature: Ceteris Paribus majority, lexicographic excellence and its dual, L (1) solution and its dual. Our main results reveal additional similarities among these five solutions and emphasize the essential features that should be considered when selecting the most appropriate solution for a given scenario. A practical application involving a bicameral legislature is also presented.

Suggested Citation

  • Michele Aleandri & Felix Fritz & Stefano Moretti, 2025. "Desirability and social ranking," Post-Print hal-05365555, HAL.
    • Handle: RePEc:hal:journl:hal-05365555
    DOI: 10.1007/s00355-025-01590-1
    Note: View the original document on HAL open archive server: https://hal.science/hal-05365555v1
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    References listed on IDEAS

    as
    1. Sébastien Courtin & Bertrand Tchantcho, 2015. "A note on the ordinal equivalence of power indices in games with coalition structure," Theory and Decision, Springer, vol. 78(4), pages 617-628, April.
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    4. Encarnación Algaba & Stefano Moretti & Eric Rémila & Philippe Solal, 2021. "Lexicographic solutions for coalitional rankings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 817-849, November.
    5. Sébastien Courtin & Bertrand Tchantcho, 2015. "A note on the ordinal equivalence of power indices in games with coalition structure," Post-Print hal-00914910, HAL.
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