Advanced Search
MyIDEAS: Login to save this article or follow this journal

The geometry of voting power: Weighted voting and hyper-ellipsoids

Contents:

Author Info

  • Houy, Nicolas
  • Zwicker, William S.
Registered author(s):

    Abstract

    Suppose legislators represent districts of varying population, and their assembly's voting rule is intended to implement the principle of one person, one vote. How should legislators' voting weights appropriately reflect these population differences? An analysis requires an understanding of the relationship between voting weight and some measure of the influence that each legislator has over collective decisions. We provide three new characterizations of weighted voting that embody this relationship. Each is based on the intuition that winning coalitions should be close to one another. The locally minimal and tightly packed characterizations use a weighted Hamming metric. Ellipsoidal separability employs the Euclidean metric: a separating hyper-ellipsoid contains all winning coalitions, and omits losing ones. The ellipsoid's proportions, and the Hamming weights, reflect the ratio of voting weight to influence, measured as Penrose–Banzhaf voting power. In particular, the spherically separable rules are those for which voting powers can serve as voting weights.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://www.sciencedirect.com/science/article/pii/S0899825613001656
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Games and Economic Behavior.

    Volume (Year): 84 (2014)
    Issue (Month): C ()
    Pages: 7-16

    as in new window
    Handle: RePEc:eee:gamebe:v:84:y:2014:i:c:p:7-16

    Contact details of provider:
    Web page: http://www.elsevier.com/locate/inca/622836

    Related research

    Keywords: Weighted voting; Voting power; Simple games; Ellipsoidal separability;

    Find related papers by JEL classification:

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Lindner, Ines & Machover, Moshe, 2004. "L.S. Penrose's limit theorem: proof of some special cases," Mathematical Social Sciences, Elsevier, vol. 47(1), pages 37-49, January.
    2. Pierre Barthelemy, Jean & Monjardet, Bernard, 1981. "The median procedure in cluster analysis and social choice theory," Mathematical Social Sciences, Elsevier, vol. 1(3), pages 235-267, May.
    3. Chang, Pao-Li & Chua, Vincent C.H. & Machover, Moshe, 2006. "L S Penrose's limit theorem: Tests by simulation," Mathematical Social Sciences, Elsevier, vol. 51(1), pages 90-106, January.
    4. Laruelle, Annick & Widgren, Mika, 1998. " Is the Allocation of Voting Power among EU States Fair?," Public Choice, Springer, vol. 94(3-4), pages 317-39, March.
    5. Taylor, Alan & Zwicker, William, 1997. "Interval measures of power," Mathematical Social Sciences, Elsevier, vol. 33(1), pages 23-74, February.
    6. Hosli, Madeleine O., 1993. "Admission of European Free Trade Association states to the European Community: effects on voting power in the European Community Council of Ministers," International Organization, Cambridge University Press, vol. 47(04), pages 629-643, September.
    7. Einy, Ezra & Lehrer, Ehud, 1989. "Regular Simple Games," International Journal of Game Theory, Springer, vol. 18(2), pages 195-207.
    8. Moshé Machover & Dan S. Felsenthal, 2001. "The Treaty of Nice and qualified majority voting," Social Choice and Welfare, Springer, vol. 18(3), pages 431-464.
    9. Dan Felsenthal & Moshé Machover, 2005. "Voting power measurement: a story of misreinvention," Social Choice and Welfare, Springer, vol. 25(2), pages 485-506, December.
    10. Gvozdeva, Tatiana & Slinko, Arkadii, 2011. "Weighted and roughly weighted simple games," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 20-30, January.
    11. Leech, Dennis, 2002. " Designing the Voting System for the Council of the European Union," Public Choice, Springer, vol. 113(3-4), pages 437-64, December.
    12. Cervone, Davide P. & Dai, Ronghua & Gnoutcheff, Daniel & Lanterman, Grant & Mackenzie, Andrew & Morse, Ari & Srivastava, Nikhil & Zwicker, William S., 2012. "Voting with rubber bands, weights, and strings," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 11-27.
    13. Lindner, Ines & Owen, Guillermo, 2007. "Cases where the Penrose limit theorem does not hold," Mathematical Social Sciences, Elsevier, vol. 53(3), pages 232-238, May.
    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 in new window

    Cited by:
    1. Sascha Kurz & Nicola Maaser & Stefan Napel & Matthias Weber, 2014. "Mostly Sunny: A Forecast of Tomorrow's Power Index Research," Tinbergen Institute Discussion Papers 14-058/I, Tinbergen Institute.

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:84:y:2014:i:c:p:7-16. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.