IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v15y1998i2p211-236.html
   My bibliography  Save this article

The paradox of multiple elections

Author

Listed:
  • Steven J. Brams

    (Department of Politics, New York University, New York, NY 10003, USA)

  • William S. Zwicker

    (Department of Mathematics, Union College, Schenectady, NY 12308, USA)

  • D. Marc Kilgour

    (Department of Mathematics, Wilfrid Laurier University Waterloo, Ontario, Canada N2L 3C5)

Abstract

Assume that voters must choose between voting yes (Y) and voting no (N) on three propositions on a referendum. If the winning combination is NYY on the first, second, and third propositions, respectively, the paradox of multiple elections is that NYY can receive the fewest votes of the 23 = 8 combinations. Several variants of this paradox are illustrated, and necessary and sufficient conditions for its occurrence, related to the "incoherence" of support, are given. The paradox is shown, via an isomorphism, to be a generalization of the well-known paradox of voting. One real-life example of the paradox involving voting on propositions in California, in which not a single voter voted on the winning side of all the propositions, is given. Several empirical examples of variants of the paradox that manifested themselves in federal elections - one of which led to divided government - and legislative votes in the US House of Representatives, are also analyzed. Possible normative implications of the paradox, such as allowing voters to vote directly for combinations using approval voting or the Borda count, are discussed.

Suggested Citation

  • Steven J. Brams & William S. Zwicker & D. Marc Kilgour, 1998. "The paradox of multiple elections," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(2), pages 211-236.
  • Handle: RePEc:spr:sochwe:v:15:y:1998:i:2:p:211-236
    Note: Received: 31 July 1996 / Accepted: 1 October 1996
    as

    Download full text from publisher

    File URL: http://link.springer.de/link/service/journals/00355/papers/8015002/80150211.pdf
    Download Restriction: Access to the full text of the articles in this series is restricted

    File URL: http://link.springer.de/link/service/journals/00355/papers/8015002/80150211.ps.gz
    Download Restriction: Access to the full text of the articles in this series is restricted

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    More about this item

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

    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:spr:sochwe:v:15:y:1998:i:2:p:211-236. 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: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: http://www.springer.com .

    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.