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When ties are possible: Weak Condorcet winners and Arrovian rationality

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  • Mostapha Diss

    (CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE], AIRESS - Africa Institute for Research in Economics and Social Sciences)

  • Keith Dougherty
  • Jac Heckelman

Abstract

We use Ehrhart polynomials to estimate the likelihood of each three-candidate social ranking produced by pairwise majority rule assuming an even number of voters and the Impartial Anonymous Culture condition. We then calculate the probability the ranking is transitive and the probability of a weak Condorcet winner. Finally, we determine the weak Condorcet efficiency of various voting rules. We prove that Baldwin, Nanson, Copeland, and ranked pairs are weak Condorcet efficient, as is Borda unless there are no ties. Simulations show that among the rest, Dowdall is typically the most efficient rule for small voter groups and anti-plurality the least.
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Suggested Citation

  • Mostapha Diss & Keith Dougherty & Jac Heckelman, 2023. "When ties are possible: Weak Condorcet winners and Arrovian rationality," Post-Print hal-04419865, HAL.
    • Handle: RePEc:hal:journl:hal-04419865
    DOI: 10.1016/j.mathsocsci.2023.03.004
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    References listed on IDEAS

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