IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2205.08368.html
   My bibliography  Save this paper

The Blocker Postulates for Measures of Voting Power

Author

Listed:
  • Arash Abizadeh
  • Adrian Vetta

Abstract

A proposed measure of voting power should satisfy two conditions to be plausible: first, it must be conceptually justified, capturing the intuitive meaning of what voting power is; second, it must satisfy reasonable postulates. This paper studies a set of postulates, appropriate for a priori voting power, concerning blockers (or vetoers) in a binary voting game. We specify and motivate five such postulates, namely, two subadditivity blocker postulates, two minimum-power blocker postulates, each in weak and strong versions, and the added-blocker postulate. We then test whether three measures of voting power, namely the classic Penrose-Banzhaf measure, the classic Shapley-Shubik index, and the newly proposed Recursive Measure, satisfy these postulates. We find that the first measure fails four of the postulates, the second fails two, while the third alone satisfies all five postulates. This work consequently adds to the plausibility of the Recursive Measure as a reasonable measure of voting power.

Suggested Citation

  • Arash Abizadeh & Adrian Vetta, 2022. "The Blocker Postulates for Measures of Voting Power," Papers 2205.08368, arXiv.org.
    • Handle: RePEc:arx:papers:2205.08368
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2205.08368
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Annick Laruelle & Federico Valenciano, 2005. "Assessing success and decisiveness in voting situations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(1), pages 171-197, January.
    2. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638.
    3. Annick Laruelle & Federico Valenciano, 2001. "Shapley-Shubik and Banzhaf Indices Revisited," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 89-104, February.
    4. Leech, Dennis, 1990. "Power Indices and Probabilistic Voting Assumptions," Public Choice, Springer, vol. 66(3), pages 293-299, September.
    5. Guillermo Owen, 1975. "Multilinear extensions and the banzhaf value," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 22(4), pages 741-750, December.
    6. Annick Laruelle & Federico Valenciano, 2005. "A critical reappraisal of some voting power paradoxes," Public Choice, Springer, vol. 125(1), pages 17-41, July.
    7. Philip Straffin, 1977. "Homogeneity, independence, and power indices," Public Choice, Springer, vol. 30(1), pages 107-118, June.
    8. Dan Felsenthal & Moshé Machover & William Zwicker, 1998. "The Bicameral Postulates and Indices of a Priori Voting Power," Theory and Decision, Springer, vol. 44(1), pages 83-116, January.
    9. František Turnovec & Jacek W. Mercik & Mariusz Mazurkiewicz, 2008. "Power Indices Methodology: Decisiveness, Pivots, and Swings," Springer Books, in: Matthew Braham & Frank Steffen (ed.), Power, Freedom, and Voting, chapter 2, pages 23-37, Springer.
    10. Dan S. Felsenthal & Moshé Machover, 2004. "A Priori Voting Power: What Is It All About?," Political Studies Review, Political Studies Association, vol. 2(1), pages 1-23, January.
    11. 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. Arash Abizadeh & Adrian Vetta, 2021. "A Recursive Measure of Voting Power that Satisfies Reasonable Postulates," Papers 2105.03006, arXiv.org, revised May 2022.
    2. 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.
    3. Arash Abizadeh & Adrian Vetta, 2022. "A General Framework for a Class of Quarrels: The Quarrelling Paradox Revisited," Papers 2205.08353, arXiv.org.
    4. Josep Freixas & Montserrat Pons, 2015. "Success and decisiveness on proper symmetric games," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(4), pages 779-794, December.
    5. 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.
    6. Friedman, Jane & Parker, Cameron, 2018. "The conditional Shapley–Shubik measure for ternary voting games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 379-390.
    7. 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.
    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. Annick Laruelle & Federico Valenciano, 2005. "A critical reappraisal of some voting power paradoxes," Public Choice, Springer, vol. 125(1), pages 17-41, July.
    10. M. Albizuri & Annick Laruelle, 2013. "An axiomatization of success," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 145-155, June.
      • Albizuri Irigoyen, Miren Iosune & Laruelle, Annick, 2011. "An axiomatization of success," IKERLANAK 6256, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    11. 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.
    12. 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.
    13. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Theory and Decision, Springer, vol. 69(1), pages 69-96, July.
    14. Matthias Weber, 2014. "Solving the Inverse Power Problem in Two-Tier Voting Settings," Tinbergen Institute Discussion Papers 14-019/I, Tinbergen Institute.
    15. Dan S. Felsenthal & Moshé Machover, 2015. "The measurement of a priori voting power," Chapters, in: Jac C. Heckelman & Nicholas R. Miller (ed.), Handbook of Social Choice and Voting, chapter 8, pages 117-139, Edward Elgar Publishing.
    16. 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.
    17. Ibarzabal, Nora & Laruelle, Annick, 2018. "Ghost seats in parliaments," European Journal of Operational Research, Elsevier, vol. 264(1), pages 354-363.
    18. 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.
    19. Abraham Diskin & Moshe Koppel, 2010. "Voting power: an information theory approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(1), pages 105-119, January.
    20. Matthias Weber, 2014. "Choosing Voting Systems behind the Veil of Ignorance: A Two-Tier Voting Experiment," Tinbergen Institute Discussion Papers 14-042/I, Tinbergen Institute.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2205.08368. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.