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


  • William Gehrlein



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

Suggested Citation

  • 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.
  • Handle: RePEc:spr:reecde:v:9:y:2005:i:4:p:317-336
    DOI: 10.1007/s10058-005-0132-z

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    Cited by:

    1. William Gehrlein & Dominique Lepelley & Issofa Moyouwou, 2015. "Voters’ preference diversity, concepts of agreement and Condorcet’s paradox," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(6), pages 2345-2368, November.
    2. William V. Gehrlein & Dominique Lepelley, 2016. "Refining measures of group mutual coherence," Quality & Quantity: International Journal of Methodology, Springer, vol. 50(4), pages 1845-1870, July.
    3. William V. Gehrlein & Dominique Lepelley & Florenz Plassmann, 2016. "Should voters be required to rank candidates in an election?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(4), pages 707-747, April.
    4. 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.
    5. Sascha Kurz & Nikolas Tautenhahn, 2013. "On Dedekind’s problem for complete simple games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 411-437, May.
    6. William Gehrlein & Dominique Lepelley, 2009. "The Unexpected Behavior of Plurality Rule," Theory and Decision, Springer, vol. 67(3), pages 267-293, September.


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