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The Unexpected Behavior of Plurality Rule

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  • William Gehrlein
  • Dominique Lepelley

Abstract

When voters' preferences on candidates are mutually coherent, in the sense that they are at all close to being perfectly single-peaked, perfectly single-troughed, or perfectly polarized, there is a large probability that a Condorcet Winner exists in elections with a small number of candidates. Given this fact, the study develops representations for Condorcet Efficiency of plurality rule as a function of the proximity of voters' preferences on candidates to being perfectly single-peaked, perfectly single-troughed or perfectly polarized. We find that the widely used plurality rule has Condorcet Efficiency values that behave in very different ways under each of these three models of mutual coherence.
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Suggested Citation

  • William Gehrlein & Dominique Lepelley, 2009. "The Unexpected Behavior of Plurality Rule," Theory and Decision, Springer, vol. 67(3), pages 267-293, September.
    • Handle: RePEc:kap:theord:v:67:y:2009:i:3:p:267-293
    DOI: 10.1007/s11238-008-9097-z
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    References listed on IDEAS

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    1. Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2008. "On Ehrhart polynomials and probability calculations in voting theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 363-383, April.
    2. Barnett,William A. & Moulin,Hervé & Salles,Maurice & Schofield,Norman J. (ed.), 1995. "Social Choice, Welfare, and Ethics," Cambridge Books, Cambridge University Press, number 9780521443401, November.
    3. Sven Berg & Bo Bjurulf, 1983. "A note on the paradox of voting: Anonymous preference profiles and May's formula," Public Choice, Springer, vol. 40(3), pages 307-316, January.
    4. Dominique Lepelley, 1994. "Condorcet efficiency of positional voting rules with single-peaked preferences," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 289-299, December.
    5. Berg, Sven, 1985. "A note on plurality distortion in large committees," European Journal of Political Economy, Elsevier, vol. 1(2), pages 271-284.
    6. William V. Gehrlein, 2002. "Obtaining representations for probabilities of voting outcomes with effectively unlimited precision integer arithmetic," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 503-512.
    7. William V. Gehrlein & Dominique Lepelley, 1999. "Condorcet efficiencies under the maximal culture condition," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(3), pages 471-490.
    8. Gehrlein, William V., 1982. "Condorcet efficiency and constant scoring rules," Mathematical Social Sciences, Elsevier, vol. 2(2), pages 123-130, March.
    9. Gehrlein, William V. & Fishburn, Peter C., 1978. "Probabilities of election outcomes for large electorates," Journal of Economic Theory, Elsevier, vol. 19(1), pages 38-49, October.
    10. William Gehrlein, 2005. "Probabilities of election outcomes with two parameters: The relative impact of unifying and polarizing candidates," Review of Economic Design, Springer;Society for Economic Design, vol. 9(4), pages 317-336, December.
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    Cited by:

    1. William Gehrlein & Dominique Lepelley, 2010. "On the probability of observing Borda’s paradox," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(1), pages 1-23, June.
    2. Brian Kogelmann, 2017. "Aggregating out of indeterminacy," Politics, Philosophy & Economics, , vol. 16(2), pages 210-232, May.

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    More about this item

    Keywords

    voting rules; Condorcet efficieny; single-peaked preferences; D7;
    All these keywords.

    JEL classification:

    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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