Abstract
Let P(n, 4) denote the probability that there is a pairwise simple majority rule winner on four candidates with n voters under the impartial anonymous culture condition. Similarly, let Pt(n, 4) denote the probability that the complete ranking obtained by pairwise simple majority voting on four candidates with n voters is transitive under the impartial anonymous culture condition. We obtain representations for P(n, 4) and Pt(n, 4), and computed values for each for odd n with 3 ≤ n ≤ 19.
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This research was supported through a fellowship from the Center for Advanced Study, University of Delaware.
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Gehrlein, W.V. Probability calculations for transitivity of simple majority rule with anonymous voters. Public Choice 66, 253–259 (1990). https://doi.org/10.1007/BF00125777
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DOI: https://doi.org/10.1007/BF00125777