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The Condorcet Efficiency Advantage that Voter Indifference Gives to Approval Voting Over Some Other Voting Rules

Author

Listed:
  • 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)

Abstract

Approval Voting is known to possess many good properties when voters have dichotomous preferences. But, when attention was restricted to the limiting case for large electorates with three candidates in an early study, Approval Voting was found to have the same Condorcet Efficiency as both Plurality Rule and Negative Plurality rule when no voter indifference is allowed in voters' preferences with the assumption of the impartial culture condition (IC). However, a later study by Diss et al. (Handbook on approval voting, 2010) shows that the introduction of any degree of indifference in an extended impartial culture condition leads to a dominance of Approval Voting over both Plurality Rule and Negative Plurality Rule on the basis of Condorcet Efficiency. Scenarios were also found for which Approval Voting had greater Condorcet Efficiency than Borda Rule. The assumptions of that study are analyzed here, and an arguably more reasonable set of assumptions leads to the conclusion that Borda Rule will dominate Approval Voting on the basis of Condorcet Efficiency for all degrees of voter indifference, except for the case of completely dichotomous preferences. The same outcome is found to result in the current study for an extended version of the Impartial Anonymous Culture Condition.

Suggested Citation

  • William V. Gehrlein & Dominique Lepelley, 2014. "The Condorcet Efficiency Advantage that Voter Indifference Gives to Approval Voting Over Some Other Voting Rules," Post-Print hal-01450834, HAL.
    • Handle: RePEc:hal:journl:hal-01450834
    DOI: 10.1007/s10726-014-9388-4
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    Cited by:

    1. Mostapha Diss & Ahmed Doghmi, 2016. "Multi-winner scoring election methods: Condorcet consistency and paradoxes," Public Choice, Springer, vol. 169(1), pages 97-116, October.
    2. Gehrlein, William V. & Lepelley, Dominique & Moyouwou, Issofa, 2016. "A note on Approval Voting and electing the Condorcet loser," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 115-122.
    3. 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.
    4. Eric Kamwa, 2023. "On Two Voting systems that combine approval and preferences: Fallback Voting and Preference Approval Voting," Working Papers hal-03614585, HAL.
    5. Durand, François & Macé, Antonin & Núñez, Matías, 2024. "Voter coordination in elections: A case for approval voting," Games and Economic Behavior, Elsevier, vol. 146(C), pages 1-34.
    6. William V. Gehrlein & Dominique Lepelley & Florenz Plassmann, 2018. "An Evaluation of the Benefit of Using Two-Stage Election Procedures," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 35(1), pages 53-79, June.
    7. Eric Kamwa, 2019. "Condorcet efficiency of the preference approval voting and the probability of selecting the Condorcet loser," Theory and Decision, Springer, vol. 87(3), pages 299-320, October.
    8. Abdelhalim El Ouafdi & Dominique Lepelley & Jérôme Serais & Hatem Smaoui, 2022. "Comparing the manipulability of approval, evaluative and plurality voting with trichotomous preferences," SN Business & Economics, Springer, vol. 2(8), pages 1-22, August.
    9. Eric Kamwa, 2023. "On two voting systems that combine approval and preferences: fallback voting and preference approval voting," Public Choice, Springer, vol. 196(1), pages 169-205, July.
    10. Begoña Subiza & Josep E. Peris, 2017. "A Representative Committee by Approval Balloting," Group Decision and Negotiation, Springer, vol. 26(5), pages 1029-1040, September.
    11. Abdelhalim El Ouafdi & Dominique Lepelley & Hatem Smaoui, 2020. "On the Condorcet efficiency of evaluative voting (and other voting rules) with trichotomous preferences," Annals of Operations Research, Springer, vol. 289(2), pages 227-241, June.
    12. Eric Kamwa, 2018. "On the Condorcet Efficiency of the Preference Approval Voting and the Probability of Selecting the Condorcet Loser," Working Papers hal-01786121, HAL.

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