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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. Saari, Donald G., 2014. "Unifying voting theory from Nakamura’s to Greenberg’s theorems," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 1-11.
    2. Mostapha Diss & William Gehrlein, 2012. "Borda’s Paradox with weighted scoring rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(1), pages 121-136, January.
    3. Saari, Donald G. & McIntee, Tomas J., 2013. "Connecting pairwise and positional election outcomes," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 140-151.
    4. 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.
    5. Davide Cervone & William Gehrlein & William Zwicker, 2005. "Which Scoring Rule Maximizes Condorcet Efficiency Under Iac?," Theory and Decision, Springer, vol. 58(2), pages 145-185, March.
    6. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521731607.
    7. Mostapha Diss & William V. Gehrlein, 2015. "The True Impact of Voting Rule Selection on Condorcet Efficiency," Economics Bulletin, AccessEcon, vol. 35(4), pages 2418-2426.
    8. William Gehrlein & Peter Fishburn, 1976. "Condorcet's paradox and anonymous preference profiles," Public Choice, Springer, vol. 26(1), pages 1-18, June.
    9. Gehrlein, William V. & Lepelley, Dominique, 2001. "The Condorcet efficiency of Borda Rule with anonymous voters," Mathematical Social Sciences, Elsevier, vol. 41(1), pages 39-50, January.
    10. Saari, Donald G., 1999. "Explaining All Three-Alternative Voting Outcomes," Journal of Economic Theory, Elsevier, vol. 87(2), pages 313-355, August.
    11. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521516051.
    12. William V. Gehrlein & Dominique Lepelley, 2011. "Voting Paradoxes and Group Coherence," Studies in Choice and Welfare, Springer, number 978-3-642-03107-6, December.
    13. Donald G. Saari & Maria M. Tataru, 1999. "The likelihood of dubious election outcomes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(2), pages 345-363.
    14. Merlin, V. & Tataru, M. & Valognes, F., 2000. "On the probability that all decision rules select the same winner," Journal of Mathematical Economics, Elsevier, vol. 33(2), pages 183-207, March.
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    Cited by:

    1. D. Marc Kilgour & Jean-Charles Grégoire & Angèle M. Foley, 2022. "Weighted scoring elections: is Borda best?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(2), pages 365-391, February.

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