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An Arrovian impossibility in combining ranking and evaluation

Author

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  • Justin Kruger

    (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)

  • M. Remzi Sanver

    (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

In a world where voters not only rank the alternatives but also qualify them as “approved” or “disapproved”, we observe that majoritarianism in preferences and majoritarianism in approvals are logically incompatible. We show that this observation generalises to the following result: every aggregation rule that respects unanimity and decomposes the aggregation of preferences and approvals is dictatorial. Our result implies an incompatibility between ordinal and evaluative approaches to social choice theory under 2 weak assumptions: respect for unanimity and independence of evaluation of each alternative. We describe possibilities when the latter assumption is relaxed. On the other hand, our impossibility generalises to the case where there are more than the two evaluative levels of “approved” and “disapproved”.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Justin Kruger & M. Remzi Sanver, 2021. "An Arrovian impossibility in combining ranking and evaluation," Post-Print hal-03347632, HAL.
    • Handle: RePEc:hal:journl:hal-03347632
    DOI: 10.1007/s00355-021-01327-w
    Note: View the original document on HAL open archive server: https://hal.science/hal-03347632v1
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    References listed on IDEAS

    as
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    Cited by:

    1. Stefano Vannucci, 2022. "Agenda manipulation-proofness, stalemates, and redundant elicitation in preference aggregation. Exposing the bright side of Arrow's theorem," Papers 2210.03200, arXiv.org.
    2. Guy Barokas & Yves Sprumont, 2022. "The broken Borda rule and other refinements of approval ranking," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(1), pages 187-199, January.
    3. Alessandro Albano & José Luis García-Lapresta & Antonella Plaia & Mariangela Sciandra, 2023. "A family of distances for preference–approvals," Annals of Operations Research, Springer, vol. 323(1), pages 1-29, April.

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