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The impact of dependence among voters’ preferences with partial indifference

Author

Listed:
  • Erik Friese

    (University of Rostock)

  • William V. Gehrlein

    (University of Delaware)

  • Dominique Lepelley

    (University of La Réunion)

  • Achill Schürmann

    (University of 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 strict rankings. This option was previously found to be a poor alternative when voters have completely independent preferences. The introduction of a small degree 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, 2017. "The impact of dependence among voters’ preferences with partial indifference," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(6), pages 2793-2812, November.
    • Handle: RePEc:spr:qualqt:v:51:y:2017:i:6:d:10.1007_s11135-016-0446-7
    DOI: 10.1007/s11135-016-0446-7
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Adrian van Deemen & Agnieszka Rusinowska, 2010. "Collective Decision Making: Views from Social Choice and Game Theory," Post-Print hal-00514840, HAL.
    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. 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.
    6. Gehrlein, William V., 1982. "Condorcet efficiency and constant scoring rules," Mathematical Social Sciences, Elsevier, vol. 2(2), pages 123-130, March.
    7. Sébastien Courtin & Mathieu Martin & Issofa Moyouwou, 2015. "The $$q$$ q -majority efficiency of positional rules," Theory and Decision, Springer, vol. 79(1), pages 31-49, July.
    8. Mostapha Diss & Patrizia Pérez-Asurmendi, 2016. "Consistent collective decisions under majorities based on difference of votes," Theory and Decision, Springer, vol. 80(3), pages 473-494, March.
    9. Fabrice Valognes & William V. Gehrlein, 2001. "Condorcet efficiency: A preference for indifference," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 193-205.
    10. Sven Berg & Bo Bjurulf, 1983. "A note on the paradox of voting: Anonymous preference profiles and May's formula," Public Choice, Springer, vol. 40(3), pages 307-316, January.
    11. Gehrlein, William V. & Lepelley, Dominique, 1998. "The Condorcet efficiency of approval voting and the probability of electing the Condorcet loser," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 271-283, April.
    12. William Gehrlein & Peter Fishburn, 1976. "Condorcet's paradox and anonymous preference profiles," Public Choice, Springer, vol. 26(1), pages 1-18, June.
    13. Adrian Van Deemen & Agnieszka Rusinowska (ed.), 2010. "Collective Decision Making," Theory and Decision Library C, Springer, number 978-3-642-02865-6, July.
    14. Fishburn, Peter C. & Gehrlein, William V., 1980. "The paradox of voting : Effects of individual indifference and intransitivity," Journal of Public Economics, Elsevier, vol. 14(1), pages 83-94, August.
    15. 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.
    16. 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.
    17. Amartya Kumar Sen, 1964. "Preferences, Votes and the Transitivity of Majority Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 31(2), pages 163-165.
    18. William Gehrlein & Fabrice Valognes, 2001. "Condorcet efficiency: A preference for indifference," Post-Print halshs-02173169, HAL.
    19. Jean-François Laslier & M. Remzi Sanver (ed.), 2010. "Handbook on Approval Voting," Studies in Choice and Welfare, Springer, number 978-3-642-02839-7, December.
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