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Connecting pairwise and positional election outcomes

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

Abstract

General conclusions relating pairwise tallies with positional (e.g., plurality, antiplurality (“vote-for-two”)) election outcomes were previously known only for the Borda Count. While it has been known since the eighteenth century that the Borda and Condorcet winners need not agree, it had not been known, for instance, in which settings the Condorcet and plurality winners can disagree, or must agree. Results of this type are developed here for all three-alternative positional rules. These relationships are based on an easily used method that connects pairwise tallies with admissible positional outcomes; e.g., a special case provides the first necessary and sufficient conditions ensuring that the Condorcet winner is the plurality winner; another case identifies when there must be a profile whereby each candidate is the “winner” with some positional rule.

Suggested Citation

  • Saari, Donald G. & McIntee, Tomas J., 2013. "Connecting pairwise and positional election outcomes," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 140-151.
    • Handle: RePEc:eee:matsoc:v:66:y:2013:i:2:p:140-151
    DOI: 10.1016/j.mathsocsci.2013.02.002
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    References listed on IDEAS

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    1. Saari, Donald G., 1989. "A dictionary for voting paradoxes," Journal of Economic Theory, Elsevier, vol. 48(2), pages 443-475, August.
    2. Sieberg, Katri & McDonald, Michael D., 2011. "Probability and Plausibility of Cycles in Three-party Systems: A Mathematical Formulation and Application," British Journal of Political Science, Cambridge University Press, vol. 41(3), pages 681-692, July.
    3. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521731607.
    4. Saari, Donald G., 1999. "Explaining All Three-Alternative Voting Outcomes," Journal of Economic Theory, Elsevier, vol. 87(2), pages 313-355, August.
    5. Donald Saari, 2010. "Systematic analysis of multiple voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(2), pages 217-247, February.
    6. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521516051.
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    Cited by:

    1. Mostapha Diss & Abdelmonaim Tlidi, 2018. "Another perspective on Borda’s paradox," Theory and Decision, Springer, vol. 84(1), pages 99-121, January.
    2. Raúl Pérez-Fernández & Bernard De Baets, 2017. "Recursive Monotonicity of the Scorix: Borda Meets Condorcet," Group Decision and Negotiation, Springer, vol. 26(4), pages 793-813, July.
    3. Dany R. DOMBOU T., 2017. "How Borda voting rule can respect Arrow IIA and avoid cloning manipulation," Journal of Economics Bibliography, KSP Journals, vol. 4(3), pages 234-243, September.
    4. 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.
    5. 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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