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How many voters are needed for paradoxes?

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  • James S. Weber

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

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    Abstract

    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.

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    Bibliographic Info

    Article provided by Springer in its journal Economic Theory.

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

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    Handle: RePEc:spr:joecth:v:20:y:2002:i:2:p:341-355

    Note: Received: April 18, 2001; revised version: May 25, 2001
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    Web page: http://link.springer.de/link/service/journals/00199/index.htm

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    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.;

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    Cited by:
    1. Giuseppe Munda, 2012. "Choosing Aggregation Rules for Composite Indicators," Social Indicators Research, Springer, vol. 109(3), pages 337-354, December.
    2. 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.
    3. 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.

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