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

How many voters are needed for paradoxes?


Author Info

  • James S. Weber

    (Department of Information and Decision Sciences, University of Illinois at Chicago, Chicago, IL 60607-7124, USA)

Registered author(s):


    This paper presents a general procedure for finding profiles with the minimum number of voters required for many important paradoxes. Borda's and Condorcet's classic examples are revisited as well as generalizations. Using Saari's procedure line, we obtain an upper bound for the minimum number of voters needed for a profile for which the Condorcet winner is not strictly top ranked for all $w_{\rm s}^{3}$ weighted positional procedures. Also we give a simple upper bound on the minimum number of voters needed for a set of prescribed voting outcomes. In contrast to situations wherein small numbers of voters are needed, we consider paradoxes requiring arbitrarily large numbers of voters as well as large numbers of alternatives. Finally we indicate connections with statistical rank based tests.

    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:
    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 under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Springer in its journal Economic Theory.

    Volume (Year): 20 (2002)
    Issue (Month): 2 ()
    Pages: 341-355

    as in new window
    Handle: RePEc:spr:joecth:v:20:y:2002:i:2:p:341-355

    Note: Received: April 18, 2001; revised version: May 25, 2001
    Contact details of provider:
    Web page:

    Order Information:

    Related research

    Keywords: Voting paradox; Minimum number of voters; Condorcet pairwise procedure; Borda Count; Plurality; $w_{\rm s}^3$ procedure; Procedure line; Committees; Kruskal-Wallis Test.;

    Find related papers by JEL classification:


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


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

    Cited by:
    1. Lee Gibson & Robert Powers, 2012. "An extension of McGarvey’s theorem from the perspective of the plurality collective choice mechanism," Social Choice and Welfare, Springer, vol. 38(1), pages 101-108, January.
    2. Giuseppe Munda, 2012. "Choosing Aggregation Rules for Composite Indicators," Social Indicators Research, Springer, vol. 109(3), pages 337-354, December.
    3. Munda, Giuseppe, 2009. "A conflict analysis approach for illuminating distributional issues in sustainability policy," European Journal of Operational Research, Elsevier, vol. 194(1), pages 307-322, April.


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


    Access and download statistics


    When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:20:y:2002:i:2:p:341-355. 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: (Guenther Eichhorn) or (Christopher F Baum).

    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.