IDEAS home Printed from https://ideas.repec.org/a/spr/grdene/v32y2023i2d10.1007_s10726-022-09809-7.html
   My bibliography  Save this article

The Generalized Shapley Value of Cooperative Games as a Social Preference Function

Author

Listed:
  • Ritu Dutta

    (Dibrugarh University)

  • Souvik Roy

    (Indian Statistical Institute)

  • Surajit Borkotokey

    (Dibrugarh University)

Abstract

We introduce a cardinal social preference rule (CSPR) which accounts for interpersonal comparisons of alternatives in groups and satisfies several desirable properties. The proposed rule transforms voters’ individual ordinal preferences to obtain a score for each alternative given by the generalized Shapley value of cooperative games with transferable utilities. Since every CSPR induces an ordinal social preference rule (OSPR) in a natural way, the score vector, we propose in our model, induces a weak preference on the set of alternatives. The proposed CSPR is characterized by using some intuitive axioms.

Suggested Citation

  • Ritu Dutta & Souvik Roy & Surajit Borkotokey, 2023. "The Generalized Shapley Value of Cooperative Games as a Social Preference Function," Group Decision and Negotiation, Springer, vol. 32(2), pages 277-300, April.
  • Handle: RePEc:spr:grdene:v:32:y:2023:i:2:d:10.1007_s10726-022-09809-7
    DOI: 10.1007/s10726-022-09809-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10726-022-09809-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10726-022-09809-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Pierre Dehez & Victor Ginsburgh, 2020. "Approval voting and Shapley ranking," Public Choice, Springer, vol. 184(3), pages 415-428, September.
    2. Nowak Andrzej S. & Radzik Tadeusz, 1994. "The Shapley Value for n-Person Games in Generalized Characteristic Function Form," Games and Economic Behavior, Elsevier, vol. 6(1), pages 150-161, January.
    3. Tobias Hiller, 2015. "The importance of players in teams of the German Bundesliga in the season 2012/2013 - a cooperative game theory approach," Applied Economics Letters, Taylor & Francis Journals, vol. 22(4), pages 324-329, March.
    4. Casajus, André, 2012. "The Shapley value without efficiency and additivity," Working Papers 114, University of Leipzig, Faculty of Economics and Management Science.
    5. Einy, Ezra & Haimanko, Ori, 2011. "Characterization of the Shapley–Shubik power index without the efficiency axiom," Games and Economic Behavior, Elsevier, vol. 73(2), pages 615-621.
    6. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    7. Amartya Sen, 2020. "Majority decision and Condorcet winners," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 211-217, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sylvain Béal & Marc Deschamps & Mostapha Diss & Rodrigue Tido Takeng, 2024. "Cooperative games with diversity constraints," Working Papers hal-04447373, HAL.
    2. M. J. Albizuri & A. Goikoetxea, 2021. "The Owen–Shapley Spatial Power Index in Three-Dimensional Space," Group Decision and Negotiation, Springer, vol. 30(5), pages 1027-1055, October.
    3. René van den Brink & Agnieszka Rusinowska, 2017. "The degree measure as utility function over positions in networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01592181, HAL.
    4. Albizuri, M.J. & Goikoetxea, A., 2022. "Probabilistic Owen-Shapley spatial power indices," Games and Economic Behavior, Elsevier, vol. 136(C), pages 524-541.
    5. Qianqian Kong & Hans Peters, 2021. "An issue based power index," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 23-38, March.
    6. Stefano Benati & Giuseppe Vittucci Marzetti, 2013. "Probabilistic spatial power indexes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 391-410, February.
    7. Ritu Dutta & Rajnish Kumnar & Surajit Borkotokey, 2023. "How to choose a Compatible Committee?," Papers 2308.03507, arXiv.org.
    8. Rodolfo Metulini & Giorgio Gnecco, 2023. "Measuring players’ importance in basketball using the generalized Shapley value," Annals of Operations Research, Springer, vol. 325(1), pages 441-465, June.
    9. André Casajus & Frank Huettner, 2019. "The Coleman–Shapley index: being decisive within the coalition of the interested," Public Choice, Springer, vol. 181(3), pages 275-289, December.
    10. Karos, Dominik & Peters, Hans, 2015. "Indirect control and power in mutual control structures," Games and Economic Behavior, Elsevier, vol. 92(C), pages 150-165.
    11. Le Breton, Michel & Lepelley, Dominique & Smaoui, Hatem, 2012. "The Probability of Casting a Decisive Vote: From IC to IAC trhough Ehrhart's Polynomials and Strong Mixing," IDEI Working Papers 722, Institut d'Économie Industrielle (IDEI), Toulouse.
    12. Roland Kirstein & Matthias Peiss, 2013. "Quantitative Machtkonzepte in der Ökonomik," FEMM Working Papers 130004, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    13. Deniz Aksoy, 2010. "Who gets what, when, and how revisited: Voting and proposal powers in the allocation of the EU budget," European Union Politics, , vol. 11(2), pages 171-194, June.
    14. Laruelle, Annick & Valenciano, Federico, 2008. "Noncooperative foundations of bargaining power in committees and the Shapley-Shubik index," Games and Economic Behavior, Elsevier, vol. 63(1), pages 341-353, May.
    15. Leech, Dennis, 2002. "Voting Power In The Governance Of The International Monetary Fund," Economic Research Papers 269354, University of Warwick - Department of Economics.
    16. Block, Joern H. & Hirschmann, Mirko & Kranz, Tobias & Neuenkirch, Matthias, 2023. "Public family firms and economic inequality across societies," Journal of Business Venturing Insights, Elsevier, vol. 19(C).
    17. Matija Kovacic & Claudio Zoli, 2021. "Ethnic distribution, effective power and conflict," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(2), pages 257-299, August.
    18. Dimitrov, Dinko & Haake, Claus-Jochen, 2011. "Coalition formation in simple Games. the semistrict core," Center for Mathematical Economics Working Papers 378, Center for Mathematical Economics, Bielefeld University.
    19. Mikel Alvarez-Mozos & José María Alonso-Meijide & María Gloria Fiestras-Janeiro, 2016. "The Shapley-Shubik Index in the Presence of Externalities," UB School of Economics Working Papers 2016/342, University of Barcelona School of Economics.
    20. László Á. Kóczy, 2016. "Power Indices When Players can Commit to Reject Coalitions," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 33(1), pages 77-91, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:grdene:v:32:y:2023:i:2:d:10.1007_s10726-022-09809-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.