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Lexicographic solutions for coalitional rankings based on individual and collective performances

Author

Listed:
  • Eric Rémila

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - Université de Lyon - UL2 - Université Lumière - Lyon 2 - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

  • Philippe Solal

  • Sylvain Béal

    (CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

Abstract

A coalitional ranking describes a situation where a finite set of agents can form coalitions that are ranked according to a weak order. A social ranking solution on a domain of coalitional rankings assigns an individual ranking, that is a weak order over the agent set, to each coalitional ranking of this domain. We introduce two lexicographic solutions for a variable population domain of coalitional rankings. These solutions are computed from the individual performance of the agents, then, when this performance criterion does not allow to decide between two agents, a collective performance criterion is applied to the coalitions of higher size. We provide parallel axiomatic characterizations of these two solutions.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Eric Rémila & Philippe Solal & Sylvain Béal, 2022. "Lexicographic solutions for coalitional rankings based on individual and collective performances," Post-Print hal-04053283, HAL.
    • Handle: RePEc:hal:journl:hal-04053283
    DOI: 10.1016/j.jmateco.2022.102738
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    Cited by:

    1. Felix Fritz & Stefano Moretti & Jochen Staudacher, 2023. "Social Ranking Problems at the Interplay between Social Choice Theory and Coalitional Games," Mathematics, MDPI, vol. 11(24), pages 1-22, December.
    2. Sylvain Béal & Sylvain Ferrières & Philippe Solal, 2023. "A Core-Partition Ranking Solution to Coalitional Ranking Problems," Group Decision and Negotiation, Springer, vol. 32(4), pages 965-985, August.
    3. Takahiro Suzuki & Masahide Horita, 2024. "Consistent social ranking solutions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 62(3), pages 549-569, May.
    4. Takahiro Suzuki & Masahide Horita, 2025. "Sabotage-proof social ranking solutions," Theory and Decision, Springer, vol. 98(2), pages 205-224, March.

    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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