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The Impact of Dependence among Voters’ Preferences with Partial Indifference

Author

Listed:
  • Erik Friese

    (Institut für Mathematik - Universität Rostock)

  • William V. Gehrlein

    (University of Delaware [Newark])

  • Dominique Lepelley

    () (CEMOI - Centre d'Économie et de Management de l'Océan Indien - UR - Université de La Réunion)

  • Achill Schürmann

    () (Institut für Mathematik - Universität Rostock)

Abstract

Standard Weighted Scoring Rules do not directly accommodate the possibility that some voters might have dichotomous preferences in three-candidate elections. The direct solution to this issue would be to require voters to arbitrarily break their indifference ties on candidates and report complete rankings. This option was previously found to be a poor alternative when voters have completely independent references. The introduction of a smalldegree of dependence among voters' preferences has typically been found to make a significant reduction of the impact of such negative outcomes in earlier studies. However, we find that the forced ranking option continues to be a poor choice when dependence is introduced among voters' preferences. This conclusion is reinforced by the fact that other voting options like Approval Voting and Extended Scoring Rules have been found to produce much better results. These observations are made as a result of using a significant advancement in techniques that obtain probability representations for such outcomes.

Suggested Citation

  • Erik Friese & William V. Gehrlein & Dominique Lepelley & Achill Schürmann, 2016. "The Impact of Dependence among Voters’ Preferences with Partial Indifference," Post-Print hal-01450829, HAL.
  • Handle: RePEc:hal:journl:hal-01450829
    DOI: 10.1007/s11135-016-0446-7
    Note: View the original document on HAL open archive server: https://hal.univ-reunion.fr/hal-01450829
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    References listed on IDEAS

    as
    1. William Gehrlein & Peter Fishburn, 1976. "Condorcet's paradox and anonymous preference profiles," Public Choice, Springer, vol. 26(1), pages 1-18, June.
    2. Kamwa, Eric & Merlin, Vincent, 2015. "Scoring rules over subsets of alternatives: Consistency and paradoxes," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 130-138.
    3. 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.
    4. Mostapha Diss & Vincent Merlin & Fabrice Valognes, 2010. "On the Condorcet Efficiency of Approval Voting and Extended Scoring Rules for Three Alternatives," Studies in Choice and Welfare, in: Jean-François Laslier & M. Remzi Sanver (ed.), Handbook on Approval Voting, chapter 0, pages 255-283, Springer.
    5. William V. Gehrlein & Dominique Lepelley, 2015. "The Condorcet Efficiency Advantage that Voter Indifference Gives to Approval Voting Over Some Other Voting Rules," Group Decision and Negotiation, Springer, vol. 24(2), pages 243-269, March.
    6. Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2008. "On Ehrhart polynomials and probability calculations in voting theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 363-383, April.
    7. Mostapha Diss & Patrizia Pérez-Asurmendi, 2015. "Consistent collective decisions under majorities based on difference of votes," Working Papers 1533, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
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