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A Core-Partition Ranking Solution to Coalitional Ranking Problems

Author

Listed:
  • Sylvain Béal

    (UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

  • Sylvain Ferrières

    (UJM - Université Jean Monnet - Saint-Étienne)

  • Philippe Solal

    (UJM - Université Jean Monnet - Saint-Étienne)

Abstract
A coalitional ranking problem is described by a weak order on the set of nonempty coalitions of a given agent set. A social ranking is a weak order on the set of agents. We consider social rankings that are consistent with stable/core partitions. A partition is stable if there is no coalition better ranked in the coalitional ranking than the rank of the cell of each of its members in the partition. The core-partition social ranking solution assigns to each coalitional ranking problem the set of social rankings such that there is a core-partition satisfying the following condition: a first agent gets a higher rank than a second agent if and only if the cell to which the first agent belongs is better ranked in the coalitional ranking than the cell to which the second agent belongs in the partition. We provide an axiomatic characterization of the core-partition social ranking and an algorithm to compute the associated social rankings.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Sylvain Béal & Sylvain Ferrières & Philippe Solal, 2023. "A Core-Partition Ranking Solution to Coalitional Ranking Problems," Post-Print hal-04114152, HAL.
    • Handle: RePEc:hal:journl:hal-04114152
    DOI: 10.1007/s10726-023-09832-2
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    References listed on IDEAS

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    1. Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), 2009. "The Mathematics of Preference, Choice and Order," Studies in Choice and Welfare, Springer, number 978-3-540-79128-7, December.
    2. Giulia Bernardi & Roberto Lucchetti & Stefano Moretti, 2019. "Ranking objects from a preference relation over their subsets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(4), pages 589-606, April.
    3. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2022. "Lexicographic solutions for coalitional rankings based on individual and collective performances," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    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. Encarnación Algaba & Stefano Moretti & Eric Rémila & Philippe Solal, 2021. "Lexicographic solutions for coalitional rankings," Post-Print hal-03422945, HAL.
    6. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    7. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    8. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
    9. Steven J. Brams & M. Remzi Sanver, 2009. "Voting Systems that Combine Approval and Preference," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 215-237, Springer.
    10. Mehmet Karakaya & Bettina Klaus, 2017. "Hedonic coalition formation games with variable populations: core characterizations and (im)possibilities," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 435-455, May.
    11. William Thomson, 2001. "On the axiomatic method and its recent applications to game theory and resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(2), pages 327-386.
    12. , & ,, 2009. "Coalition formation under power relations," Theoretical Economics, Econometric Society, vol. 4(1), March.
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    JEL classification:

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

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