Advanced Search
MyIDEAS: Login to save this paper or follow this series

Social Indeterminacy

Contents:

Author Info

  • Gil Kalai

    ()

Registered author(s):

    Abstract

    An extension of Condorcet's paradox by McGarvey (1953) asserts that for every asymmetric relation R on a finite set of candidates there is a strict-preferences voter profile that has the relation R as its strict simple majority relation. We prove that McGarvey's theorem can be extended to arbitrary neutral monotone social welfare functions which can be described by a strong simple game G if the voting power of each individual, measured by the it Shapley-Shubik power index, is sufficiently small. Our proof is based on an extension to another classic result concerning the majority rule. Condorcet studied an election between two candidates in which the voters' choices are random and independent and the probability of a voter choosing the first candidate is p > 1/2. Condorcet's Jury Theorem asserts that if the number of voters tends to infinity then the probability that the first candidate will be elected tends to one. We prove that this assertion extends to a sequence of arbitrary monotone strong simple games if and only if the maximum voting power for all individuals tends to zero.

    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://ratio.huji.ac.il/sites/default/files/publications/dp362.pdf
    Download Restriction: no

    Bibliographic Info

    Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp362.

    as in new window
    Length: 38 pages
    Date of creation: Jun 2004
    Date of revision:
    Publication status: Published in Econometrica, 2004, vol. 72, pp. 1565-1581.
    Handle: RePEc:huj:dispap:dp362

    Contact details of provider:
    Postal: Feldman Building - Givat Ram - 91904 Jerusalem
    Phone: +972-2-6584135
    Fax: +972-2-6513681
    Email:
    Web page: http://www.ratio.huji.ac.il/
    More information through EDIRC

    Related research

    Keywords: social choice; information aggregation; Arrow's theorem; simple games; the Shapley-Shubik power index; threshold phenomena;

    Find related papers by JEL classification:

    This paper has been announced in the following NEP Reports:

    References

    No references listed on IDEAS
    You can help add them by filling out this form.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as in new window

    Cited by:
    1. Olle Haggstrom & Gil Kalai & Elchanan Mossel, 2004. "A Law of Large Numbers for Weighted Majority," Discussion Paper Series dp363, The Center for the Study of Rationality, Hebrew University, Jerusalem.
    2. Beigman, Eyal, 2010. "Simple games with many effective voters," Games and Economic Behavior, Elsevier, vol. 68(1), pages 15-22, January.
    3. Joe Neeman, 2014. "A law of large numbers for weighted plurality," Social Choice and Welfare, Springer, vol. 42(1), pages 99-109, January.

    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:huj:dispap:dp362. 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: (Ilan Nehama).

    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.