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Probabilities of election outcomes with two parameters: The relative impact of unifying and polarizing candidates

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  • William Gehrlein

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    Abstract

    Consider an election on three candidates for n voters with complete and transitive preference rankings on the candidates. Let k (r) denote the minimum total number of last (middle) position rankings for each of the three candidates. If k is close to zero, some candidate is seldom disliked and is a unifying candidate. If r is close to zero, some candidate is always either liked or disliked and is a polarizing candidate. A procedure is developed to obtain representations for conditional probabilities of election outcomes, when parameters like k or r are specified. Representations are obtained for the conditional probability that a pairwise majority rule winner, or PMRW, exists, given k and given r. Results show significant differences in the impact that unifying and polarizing candidates have on the probability that a PMRW exists. Copyright Springer-Verlag Berlin/Heidelberg 2005

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    Bibliographic Info

    Article provided by Springer in its journal Review of Economic Design.

    Volume (Year): 9 (2005)
    Issue (Month): 4 (December)
    Pages: 317-336

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    Handle: RePEc:spr:reecde:v:9:y:2005:i:4:p:317-336

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    Related research

    Keywords: Condorcet winner; probability Condorcet winner; probability;

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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, vol. 35(1), pages 1-23, June.
    2. William Gehrlein & Dominique Lepelley, 2009. "The Unexpected Behavior of Plurality Rule," Theory and Decision, Springer, vol. 67(3), pages 267-293, September.
    3. Sascha Kurz & Nikolas Tautenhahn, 2013. "On Dedekind’s problem for complete simple games," International Journal of Game Theory, Springer, vol. 42(2), pages 411-437, May.

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