IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v101y2025i3d10.1007_s00186-025-00895-2.html

Spatial Power Indices with a Finite Number of Issues

Author

Listed:
  • M. Josune Albizuri

    (University of the Basque Country)

  • Alex Goikoetxea

    (University of the Basque Country)

  • Jose M. Zarzuelo

    (University of the Basque Country)

Abstract

The Owen-Shapley spatial power index measures the power in a voting situation taking into account the ideological location of the voters. This spatial index assumes that voters face a continuum of issues, and these issues have the same relevance, and therefore are equally likely. In this work, we introduce a family of spatial power indices, where each member of the family is a modified version of the Owen-Shapley spatial power index. Unlike the case of the Owen-Shapley index, in this paper, we consider a more realistic assumption, namely, that voters face a finite number of issues and that these issues may have different relevance. Additionally, we provide an axiomatic characterization of this family using three basic axioms: equal power change property, anonymity, and dummy player property. Furthermore, we prove that these axioms are independent. Finally, an application for the Basque Parliament after the 2020 elections is also provided to study the distribution of power among the parties.

Suggested Citation

  • M. Josune Albizuri & Alex Goikoetxea & Jose M. Zarzuelo, 2025. "Spatial Power Indices with a Finite Number of Issues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 101(3), pages 373-394, June.
    • Handle: RePEc:spr:mathme:v:101:y:2025:i:3:d:10.1007_s00186-025-00895-2
    DOI: 10.1007/s00186-025-00895-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-025-00895-2
    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/s00186-025-00895-2?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

    for a different version of it.

    References listed on IDEAS

    as
    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. Owen, G & Shapley, L S, 1989. "Optimal Location of Candidates in Ideological Space," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 339-356.
    3. Martin, Mathieu & Nganmeni, Zephirin & Tchantcho, Bertrand, 2017. "The Owen and Shapley spatial power indices: A comparison and a generalization," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 10-19.
    4. Guillermo Owen, 1975. "Multilinear extensions and the banzhaf value," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 22(4), pages 741-750, December.
    5. Francesco Passarelli & Jason Barr, 2007. "Preferences, the Agenda Setter, and the Distribution of Power in the EU," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 41-60, January.
    6. Dubey, Pradeep & Einy, Ezra & Haimanko, Ori, 2005. "Compound voting and the Banzhaf index," Games and Economic Behavior, Elsevier, vol. 51(1), pages 20-30, April.
    7. 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.
    8. Ezra Einy, 1987. "Semivalues of Simple Games," Mathematics of Operations Research, INFORMS, vol. 12(2), pages 185-192, May.
    9. Shenoy, Prakash P., 1982. "The Banzhaf power index for political games," Mathematical Social Sciences, Elsevier, vol. 2(3), pages 299-315, April.
    10. Monroy, Luisa & Fernández, Francisco R., 2011. "The Shapley-Shubik index for multi-criteria simple games," European Journal of Operational Research, Elsevier, vol. 209(2), pages 122-128, March.
    11. Hans Peters & José M. Zarzuelo, 2017. "An axiomatic characterization of the Owen–Shapley spatial power index," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 525-545, May.
    12. Freixas, Josep & Kurz, Sascha, 2016. "The cost of getting local monotonicity," European Journal of Operational Research, Elsevier, vol. 251(2), pages 600-612.
    13. Guillermo Owen & Francesc Carreras, 2022. "Spatial games and endogenous coalition formation," Annals of Operations Research, Springer, vol. 318(2), pages 1095-1115, November.
    14. 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.
    15. Freixas, Josep & Kaniovski, Serguei, 2014. "The minimum sum representation as an index of voting power," European Journal of Operational Research, Elsevier, vol. 233(3), pages 739-748.
    16. 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.
    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. Albizuri, M.J. & Goikoetxea, A., 2022. "Probabilistic Owen-Shapley spatial power indices," Games and Economic Behavior, Elsevier, vol. 136(C), pages 524-541.
    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. 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.
    4. Hans Peters & José M. Zarzuelo, 2017. "An axiomatic characterization of the Owen–Shapley spatial power index," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 525-545, May.
    5. Arnold Cédrick SOH VOUTSA, 2020. "Deegan-Packel & Johnston spatial power indices and characterizations," Thema Working Papers 2020-16, THEMA (Théorie Economique, Modélisation et Applications), CY Cergy-Paris University, ESSEC and CNRS.
    6. Martin, Mathieu & Nganmeni, Zephirin & Tchantcho, Bertrand, 2017. "The Owen and Shapley spatial power indices: A comparison and a generalization," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 10-19.
    7. Philip D. Grech, 2021. "Power in the Council of the EU: organizing theory, a new index, and Brexit," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(2), pages 223-258, February.
    8. Béal, Sylvain & Deschamps, Marc & Diss, Mostapha & Tido Takeng, Rodrigue, 2025. "Cooperative games with diversity constraints," Journal of Mathematical Economics, Elsevier, vol. 116(C).
    9. Stefano Benati & Giuseppe Vittucci Marzetti, 2021. "Voting power on a graph connected political space with an application to decision-making in the Council of the European Union," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 733-761, November.
    10. Kong, Qianqian & Peters, Hans, 2023. "Power indices for networks, with applications to matching markets," European Journal of Operational Research, Elsevier, vol. 306(1), pages 448-456.
    11. Ori Haimanko, 2019. "The Banzhaf Value and General Semivalues for Differentiable Mixed Games," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 767-782, August.
    12. 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.
    13. Arnold Cédrick SOH VOUTSA, 2021. "The Public Good spatial power index in political games," Thema Working Papers 2021-01, THEMA (Théorie Economique, Modélisation et Applications), CY Cergy-Paris University, ESSEC and CNRS.
    14. Ori Haimanko, 2025. "On subgame consistency of the Shapley-Shubik power index," International Journal of Game Theory, Springer;Game Theory Society, vol. 54(2), pages 1-20, December.
    15. Benati, Stefano & Rizzi, Romeo & Tovey, Craig, 2015. "The complexity of power indexes with graph restricted coalitions," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 53-63.
    16. Ori Haimanko, 2019. "Composition independence in compound games: a characterization of the Banzhaf power index and the Banzhaf value," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(3), pages 755-768, September.
    17. Haimanko, Ori, 2018. "The axiom of equivalence to individual power and the Banzhaf index," Games and Economic Behavior, Elsevier, vol. 108(C), pages 391-400.
    18. Gusev, Vasily V., 2020. "The vertex cover game: Application to transport networks," Omega, Elsevier, vol. 97(C).
    19. 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.
    20. Ori Haimanko, 2020. "Generalized Coleman-Shapley indices and total-power monotonicity," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 299-320, March.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

    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:spr:mathme:v:101:y:2025:i:3:d:10.1007_s00186-025-00895-2. 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.