IDEAS home Printed from https://ideas.repec.org/p/huj/dispap/dp362.html
   My bibliography  Save this paper

Social Indeterminacy

Author

Listed:
  • Gil Kalai

    ()

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.

Suggested Citation

  • Gil Kalai, 2004. "Social Indeterminacy," Discussion Paper Series dp362, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp362
    as

    Download full text from publisher

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

    Citations

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


    Cited by:

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

    More about this item

    Keywords

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

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

    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: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: (Michael Simkin). General contact details of provider: http://edirc.repec.org/data/crihuil.html .

    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.

    We have no references for this item. You can help adding them by using 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.