IDEAS home Printed from https://ideas.repec.org/a/wsi/igtrxx/v15y2013i02ns0219198913400045.html
   My bibliography  Save this article

Comparing Power Indices

Author

Listed:
  • CESARINO BERTINI

    (Department of Management, Economics and Quantitative Methods, University of Bergamo, via dei Caniana 2, 24127 Bergamo, Italy)

  • JOSEP FREIXAS

    (Department of Applied Mathematics III and High Engineering School, (Manresa Campus), Technical University of Catalonia, Av. de les Bases de Manresa, 71-73 Manresa, Spain)

  • GIANFRANCO GAMBARELLI

    (Department of Management, Economics and Quantitative Methods, University of Bergamo, via dei Caniana 2, 24127 Bergamo, Italy)

  • IZABELLA STACH

    (AGH University of Science and Technology, Faculty of Management, ul. Gramatyka 10, 30-067 Krakow, Poland)

Abstract

This paper aims to give a global vision concerning the state of the art of studies on 13 power indices and to establish which of them are more suitable for describing the real situations which are, from time to time, taken into consideration. In such contexts, different comparisons have been developed in terms of properties, axiomatic grounds and so on. This analysis points out various open problems.

Suggested Citation

  • Cesarino Bertini & Josep Freixas & Gianfranco Gambarelli & Izabella Stach, 2013. "Comparing Power Indices," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-19.
    • Handle: RePEc:wsi:igtrxx:v:15:y:2013:i:02:n:s0219198913400045
    DOI: 10.1142/S0219198913400045
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219198913400045
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219198913400045?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. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638, November.
    2. Laruelle, Annick & Albizuri Irigoyen, Miren Iosune, 2011. "An axiomatization of success," IKERLANAK 2011-49, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    3. 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.
    4. repec:ehu:ikerla:6256 is not listed on IDEAS
    5. Gianfranco Gambarelli & Guillermo Owen, 2004. "The Coming of Game Theory," Theory and Decision, Springer, vol. 56(2_2), pages 1-18, February.
    6. Robert P. Gilles, 2010. "The Cooperative Game Theory of Networks and Hierarchies," Theory and Decision Library C, Springer, number 978-3-642-05282-8, December.
    7. Gianfranco Gambarelli & Guillermo Owen, 2004. "The Coming of Game Theory," Theory and Decision, Springer, vol. 56(1), pages 1-18, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Izabella Stach, 2022. "Reformulation of Public Help Index θ Using Null Player Free Winning Coalitions," Group Decision and Negotiation, Springer, vol. 31(2), pages 317-334, April.
    2. Karos, Dominik & Peters, Hans, 2018. "Effectivity and power," Games and Economic Behavior, Elsevier, vol. 108(C), pages 363-378.
    3. Izabella Stach & Jacek Mercik, 2021. "Measurement of control power in corporate networks," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 31, pages 97-121.
    4. Jochen Staudacher & Felix Wagner & Jan Filipp, 2021. "Dynamic Programming for Computing Power Indices for Weighted Voting Games with Precoalitions," Games, MDPI, vol. 13(1), pages 1-17, December.
    5. Aleksei Y. Kondratev & Vladimir V. Mazalov, 2020. "Tournament solutions based on cooperative game theory," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 119-145, March.
    6. 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.
    7. Izabella Stach & Jacek Mercik, 2021. "Measurement of control power in corporate networks," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(1), pages 97-121.
    8. 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.
    9. Somdeb Lahiri, 2021. "Pattanaik's axioms and the existence of winners preferred with probability at least half," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(2), pages 109-122.

    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. 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.
    2. 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.
    3. Sylvain Béal & Marc Deschamps & Mostapha Diss & Rodrigue Tido Takeng, 2024. "Cooperative games with diversity constraints," Working Papers hal-04447373, HAL.
    4. Lukáš Adam & Tomáš Kroupa, 2017. "The intermediate set and limiting superdifferential for coalitional games: between the core and the Weber set," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 891-918, November.
    5. Stephan Michel & Ignacio N. Cofone, 2017. "Majority Rules in Constitutional Referendums," Kyklos, Wiley Blackwell, vol. 70(3), pages 402-424, August.
    6. Sridhar Mandyam & Usha Sridhar, 2017. "DON and Shapley Value for Allocation among Cooperating Agents in a Network: Conditions for Equivalence," Studies in Microeconomics, , vol. 5(2), pages 143-161, December.
    7. Le Breton, Michel & Montero, Maria & Zaporozhets, Vera, 2012. "Voting power in the EU council of ministers and fair decision making in distributive politics," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 159-173.
    8. Fabrice Barthelemy & Mathieu Martin, 2011. "A Comparison Between the Methods of Apportionment Using Power Indices: the Case of the US Presidential Elections," Annals of Economics and Statistics, GENES, issue 101-102, pages 87-106.
    9. Stefan Napel & Mika Widgrén, 2011. "Strategic versus non-strategic voting power in the EU Council of Ministers: the consultation procedure," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(3), pages 511-541, September.
    10. René Brink & Frank Steffen, 2012. "Axiomatizations of a positional power score and measure for hierarchies," Public Choice, Springer, vol. 151(3), pages 757-787, June.
    11. Sébastien Courtin & Zéphirin Nganmeni & Bertrand Tchantcho, 2016. "The Shapley–Shubik power index for dichotomous multi-type games," Theory and Decision, Springer, vol. 81(3), pages 413-426, September.
    12. Courtin, Sébastien & Nganmeni, Zéphirin & Tchantcho, Bertrand, 2017. "Dichotomous multi-type games with a coalition structure," Mathematical Social Sciences, Elsevier, vol. 86(C), pages 9-17.
    13. Fabrice Barthelemy & Mathieu Martin & Bertrand Tchantcho, 2011. "Some conjectures on the two main power indices," THEMA Working Papers 2011-14, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    14. Bhattacherjee, Sanjay & Chakravarty, Satya R. & Sarkar, Palash, 2022. "A General Model for Multi-Parameter Weighted Voting Games," MPRA Paper 115407, University Library of Munich, Germany.
    15. 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.
    16. Vasily V. Gusev, 2021. "Set-weighted games and their application to the cover problem," HSE Working papers WP BRP 247/EC/2021, National Research University Higher School of Economics.
    17. Sébastien Courtin & Zephirin Nganmeni & Bertrand Tchantcho, 2015. "Dichotomous multi-type games: Shapley-Shubik and Banzhaf-Coleman power indices," THEMA Working Papers 2015-05, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    18. 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.
    19. Josep Freixas & Montserrat Pons, 2017. "Using the Multilinear Extension to Study Some Probabilistic Power Indices," Group Decision and Negotiation, Springer, vol. 26(3), pages 437-452, May.
    20. Pongou, Roland & Tchantcho, Bertrand & Tedjeugang, Narcisse, 2014. "Power theories for multi-choice organizations and political rules: Rank-order equivalence," Operations Research Perspectives, Elsevier, vol. 1(1), pages 42-49.

    More about this item

    Keywords

    Cooperative games; power indices; simple games; voting; 91A06; 91A12; 91B12;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

    Statistics

    Access and download statistics

    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:wsi:igtrxx:v:15:y:2013:i:02:n:s0219198913400045. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/igtr/igtr.shtml .

    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.