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Likelihood of voting outcomes with generalized IAC probabilities

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  • McIntee, Tomas J.
  • Saari, Donald G.

Abstract

After determining all supporting profiles with any number of voters for any specified three-candidate pairwise majority vote outcome, a new, large class of “octahedral” probability distributions, motivated by and including IAC, is introduced to examine various three-candidate voting outcomes involving majority vote outcomes. Illustrating examples include computing each distribution’s likelihood of a majority vote cycle and the likelihood that the Borda Count and Condorcet winners agree. Surprisingly, computations often reduce to a simple exercise of finding the volumes of tetrahedrons.

Suggested Citation

  • McIntee, Tomas J. & Saari, Donald G., 2017. "Likelihood of voting outcomes with generalized IAC probabilities," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 1-10.
  • Handle: RePEc:eee:matsoc:v:87:y:2017:i:c:p:1-10
    DOI: 10.1016/j.mathsocsci.2017.01.003
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    References listed on IDEAS

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    1. William Gehrlein & Peter Fishburn, 1976. "Condorcet's paradox and anonymous preference profiles," Public Choice, Springer, vol. 26(1), pages 1-18, June.
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    6. Saari, Donald G. & McIntee, Tomas J., 2013. "Connecting pairwise and positional election outcomes," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 140-151.
    7. Donald G. Saari, 2001. "Analyzing a nail-biting election," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 415-430.
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