IDEAS home Printed from https://ideas.repec.org/p/rif/dpaper/707.html
   My bibliography  Save this paper

On the Probabilistic Relationship between the Public Good Index and the Normalized Banzhaf Index

Author

Listed:
  • WidgrÉn, Mika

Abstract

In this paper we develop a probablistic interpretation for the normalized Banzhaf index and the public good index. We then derive a way to decompose the normalized Banzhaf index into two parts. The first of them relates the Banzhaf index with the public good index and the other one on a special type of luck. Similarities and differences of the two indices are then discussed.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • WidgrÉn, Mika, 2002. "On the Probabilistic Relationship between the Public Good Index and the Normalized Banzhaf Index," Discussion Papers 707, The Research Institute of the Finnish Economy.
    • Handle: RePEc:rif:dpaper:707
    as

    Download full text from publisher

    File URL: http://www.etla.fi/wp-content/uploads/2012/09/dp707.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Leech, Dennis, 1990. "Power Indices and Probabilistic Voting Assumptions," Public Choice, Springer, vol. 66(3), pages 293-299, September.
    2. Steven J. Brams & Peter C. Fishburn, 1996. "Minimal winning coalitions in weighted-majority voting games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(4), pages 397-417.
    3. Philip Straffin, 1977. "Homogeneity, independence, and power indices," Public Choice, Springer, vol. 30(1), pages 107-118, June.
    4. Manfred J. Holler, 1998. "Two Stories, One Power Index," Journal of Theoretical Politics, , vol. 10(2), pages 179-190, April.
    5. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    6. Steven J. Brams & Peter C. Fishburn, 1995. "When is Size a Liability?," Journal of Theoretical Politics, , vol. 7(3), pages 301-316, July.
    7. Annick Laruelle, 1999. "- On The Choice Of A Power Index," Working Papers. Serie AD 1999-10, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    8. 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.
    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. Manfred Holler & Rie Ono & Frank Steffen, 2001. "Constrained Monotonicity and the Measurement of Power," Theory and Decision, Springer, vol. 50(4), pages 383-395, June.
    2. Arash Abizadeh & Adrian Vetta, 2021. "A Recursive Measure of Voting Power that Satisfies Reasonable Postulates," Papers 2105.03006, arXiv.org, revised May 2022.
    3. Donal G. Saari & Katri K. Sieberg, 1999. "Some Surprising Properties of Power Indices," Discussion Papers 1271, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. 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.
    5. Serguei Kaniovski, 2008. "The exact bias of the Banzhaf measure of power when votes are neither equiprobable nor independent," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(2), pages 281-300, August.
    6. 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.
    7. Carreras, Francesc, 2005. "A decisiveness index for simple games," European Journal of Operational Research, Elsevier, vol. 163(2), pages 370-387, June.
    8. René Brink & Agnieszka Rusinowska & Frank Steffen, 2013. "Measuring power and satisfaction in societies with opinion leaders: an axiomatization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 671-683, September.
    9. Barua, Rana & Chakravarty, Satya R. & Roy, Sonali & Sarkar, Palash, 2004. "A characterization and some properties of the Banzhaf-Coleman-Dubey-Shapley sensitivity index," Games and Economic Behavior, Elsevier, vol. 49(1), pages 31-48, October.
    10. Laruelle, Annick & Valenciano, Federico, 2002. "Inequality among EU citizens in the EU's Council decision procedure," European Journal of Political Economy, Elsevier, vol. 18(3), pages 475-498, September.
    11. Madeleine Hosli & Rebecca Moody & Bryan O’Donovan & Serguei Kaniovski & Anna Little, 2011. "Squaring the circle? Collective and distributive effects of United Nations Security Council reform," The Review of International Organizations, Springer, vol. 6(2), pages 163-187, July.
    12. Arash Abizadeh & Adrian Vetta, 2022. "The Blocker Postulates for Measures of Voting Power," Papers 2205.08368, arXiv.org.
    13. Diana Cheng & Peter Coughlin, 2017. "Using equations from power indices to analyze figure skating teams," Public Choice, Springer, vol. 170(3), pages 231-251, March.
    14. René van den Brink & Agnieszka Rusinowska & Frank Steffen, 2009. "Measuring Power and Satisfaction in Societies with Opinion Leaders: Dictator and Opinion Leader Properties," Tinbergen Institute Discussion Papers 09-052/1, Tinbergen Institute.
    15. Zineb Abidi & Matthieu Leprince & Vincent Merlin, 2020. "Power Inequality in Inter-communal Structures: The Simulated Impact of a Reform in the Case of the Municipalities in Western France," Post-Print halshs-02996998, HAL.
    16. Dennis Leech, 2002. "An Empirical Comparison of the Performance of Classical Power Indices," Political Studies, Political Studies Association, vol. 50(1), pages 1-22, March.
    17. Mika WidgrÚn & Stefan Napel, 2002. "The Power of a Spatially Inferior Player," Homo Oeconomicus, Institute of SocioEconomics, vol. 19, pages 327-343.
    18. Artyom Jelnov & Pavel Jelnov, 2019. "Success, Survival and Probabilistic Voting: The Case of a ruling Party," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 36(3), pages 209-226, December.
    19. Napel, Stefan & Widgrén, Mika, 2017. "Power measurement as sensitivity analysis: a unified approach," Center for Mathematical Economics Working Papers 345, Center for Mathematical Economics, Bielefeld University.
    20. Kóczy, László Á., 2012. "Beyond Lisbon: Demographic trends and voting power in the European Union Council of Ministers," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 152-158.

    More about this item

    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:rif:dpaper:707. 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: Kaija Hyvönen-Rajecki (email available below). General contact details of provider: https://edirc.repec.org/data/etlaafi.html .

    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.