IDEAS home Printed from https://ideas.repec.org/a/sae/jothpo/v10y1998i2p179-190.html
   My bibliography  Save this article

Two Stories, One Power Index

Author

Listed:
  • Manfred J. Holler

Abstract

This paper demonstrates that the mathematical properties of the member bargaining power measure (MBP) are identical with those of the public good index (PGI). However, the underlying theoretical concepts of the two measures are different. The MBP refers to bargaining over shares of the coalition value, and thus has a private good perspective, whereas the PGI considers power with respect to providing a public good as coalition value. The identity of the mathematical properties is used to study the properties of the two measures. For weighted voting games, both measures violate monotonicity with respect to voting weights, and the paradox of weighted voting applies.

Suggested Citation

  • Manfred J. Holler, 1998. "Two Stories, One Power Index," Journal of Theoretical Politics, , vol. 10(2), pages 179-190, April.
    • Handle: RePEc:sae:jothpo:v:10:y:1998:i:2:p:179-190
    DOI: 10.1177/0951692898010002002
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/0951692898010002002
    Download Restriction: no
    File URL: https://libkey.io/10.1177/0951692898010002002?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
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Steven J. Brams & Peter C. Fishburn, 1995. "When is Size a Liability?," Journal of Theoretical Politics, , vol. 7(3), pages 301-316, July.
    3. 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.
    4. Turnovec, Frantisek, 1997. "Monotonicity of Power Indices," East European Series 41, Institute for Advanced Studies.
    5. Dietrich Fischer & Andrew Schotter, 1978. "The inevitability of the “paradox of redistribution” in the allocation of voting weights," Public Choice, Springer, vol. 33(2), pages 49-67, September.
    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. Mika WidgrÚn, 2002. "On the Probablistic Relationship between the Public Good Index and the Normalized Bannzhaf Index," Homo Oeconomicus, Institute of SocioEconomics, vol. 19, pages 373-386.
    2. Fabi'an Riquelme & Pablo Gonz'alez-Cantergiani & Gabriel Godoy, 2018. "Voting power of political parties in the Senate of Chile during the whole binomial system period: 1990-2017," Papers 1808.07854, arXiv.org, revised Sep 2019.

    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. José María Alonso‐Meijide & Manfred J. Holler, 2009. "Freedom Of Choice And Weighted Monotonicity Of Power," Metroeconomica, Wiley Blackwell, vol. 60(4), pages 571-583, November.
    3. Michela Chessa, 2014. "A generating functions approach for computing the Public Good index efficiently," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 658-673, July.
    4. Mika WidgrÚn, 2002. "On the Probablistic Relationship between the Public Good Index and the Normalized Bannzhaf Index," Homo Oeconomicus, Institute of SocioEconomics, vol. 19, pages 373-386.
    5. Michel Grabisch & Agnieszka Rusinowska, 2010. "Different Approaches to Influence Based on Social Networks and Simple Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00514850, HAL.
    6. Geir Asheim & Carl Claussen & Tore Nilssen, 2006. "Majority voting leads to unanimity," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(1), pages 91-110, December.
    7. Thomas Bräuninger & Thomas König, 2000. "Making Rules for Governing Global Commons," Journal of Conflict Resolution, Peace Science Society (International), vol. 44(5), pages 604-629, October.
    8. Francesc Carreras & Antonio Magaña, 2008. "The Shapley–Shubik index for simple games with multiple alternatives," Annals of Operations Research, Springer, vol. 158(1), pages 81-97, February.
    9. Debabrata Pal, 2021. "Does everyone have equal voting power?," Indian Economic Review, Springer, vol. 56(2), pages 515-525, December.
    10. František Turnovec, 2007. "New Measure of Voting Power," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 1(1), pages 04-14, March.
    11. J. Alonso-Meijide & C. Bowles & M. Holler & S. Napel, 2009. "Monotonicity of power in games with a priori unions," Theory and Decision, Springer, vol. 66(1), pages 17-37, January.
    12. Kurz, Sascha & Mayer, Alexander & Napel, Stefan, 2020. "Weighted committee games," European Journal of Operational Research, Elsevier, vol. 282(3), pages 972-979.
    13. Braham, Matthew & Steffen, Frank, 2002. "Voting rules in insolvency law: a simple-game theoretic approach," International Review of Law and Economics, Elsevier, vol. 22(4), pages 421-442, December.
    14. Matthias Sutter, 2000. "Flexible Integration, EMU and Relative Voting Power in the EU," Public Choice, Springer, vol. 104(1), pages 41-62, July.
    15. Frits Hof & Walter Kern & Sascha Kurz & Kanstantsin Pashkovich & Daniël Paulusma, 2020. "Simple games versus weighted voting games: bounding the critical threshold value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(4), pages 609-621, April.
    16. 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.
    17. Sylvain Béal & Marc Deschamps & Mostapha Diss & Rodrigue Tido Takeng, 2024. "Cooperative games with diversity constraints," Working Papers hal-04447373, HAL.
    18. Roland Kirstein & Matthias Peiss, 2013. "Quantitative Machtkonzepte in der Ökonomik," FEMM Working Papers 130004, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    19. 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.
    20. 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.

    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:sae:jothpo:v:10:y:1998:i:2:p:179-190. 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: SAGE Publications (email available below). General contact details of provider: .

    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.