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How frequently do different voting rules encounter voting paradoxes in three-candidate elections?

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  • Florenz Plassmann

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  • T. Tideman

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Abstract

We estimate the frequencies with which ten voting anomalies (ties and nine voting paradoxes) occur under 14 voting rules, using a statistical model that simulates voting situations that follow the same distribution as voting situations in actual elections. Thus the frequencies that we estimate from our simulated data are likely to be very close to the frequencies that would be observed in actual three-candidate elections. We find that two Condorcet-consistent voting rules do, the Black rule and the Nanson rule, encounter most paradoxes and ties less frequently than the other rules do, especially in elections with few voters. The Bucklin rule, the Plurality rule, and the Anti-plurality rule tend to perform worse than the other eleven rules, especially when the number of voters becomes large. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Florenz Plassmann & T. Tideman, 2014. "How frequently do different voting rules encounter voting paradoxes in three-candidate elections?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 31-75, January.
  • Handle: RePEc:spr:sochwe:v:42:y:2014:i:1:p:31-75
    DOI: 10.1007/s00355-013-0720-8
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Conal Duddy, 2017. "Geometry of run-off elections," Public Choice, Springer, vol. 173(3), pages 267-288, December.
    3. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2020. "On Some k -scoring Rules for Committee Elections: Agreement and Condorcet Principle," Revue d'économie politique, Dalloz, vol. 130(5), pages 699-725.
    4. Aleksei Y. Kondratev & Alexander S. Nesterov, 2020. "Measuring majority power and veto power of voting rules," Public Choice, Springer, vol. 183(1), pages 187-210, April.
    5. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2019. "On some k-scoring rules for committee elections: agreement and Condorcet Principle," Working Papers hal-02147735, HAL.
    6. 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.
    7. Dominique Lepelley & Issofa Moyouwou & Hatem Smaoui, 2018. "Monotonicity paradoxes in three-candidate elections using scoring elimination rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 1-33, January.
    8. Jac C. Heckelman & Nicholas R. Miller (ed.), 2015. "Handbook of Social Choice and Voting," Books, Edward Elgar Publishing, number 15584.
    9. Marek M. Kaminski, 2015. "Empirical examples of voting paradoxes," Chapters, in: Jac C. Heckelman & Nicholas R. Miller (ed.), Handbook of Social Choice and Voting, chapter 20, pages 367-387, Edward Elgar Publishing.
    10. D. Marc Kilgour & Jean-Charles Grégoire & Angèle M. Foley, 2020. "The prevalence and consequences of ballot truncation in ranked-choice elections," Public Choice, Springer, vol. 184(1), pages 197-218, July.
    11. Moyouwou, Issofa & Tchantcho, Hugue, 2017. "Asymptotic vulnerability of positional voting rules to coalitional manipulation," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 70-82.
    12. Nicholas R. Miller, 2017. "Closeness matters: monotonicity failure in IRV elections with three candidates," Public Choice, Springer, vol. 173(1), pages 91-108, October.
    13. Dougherty, Keith L. & Heckelman, Jac C., 2020. "The probability of violating Arrow’s conditions," European Journal of Political Economy, Elsevier, vol. 65(C).
    14. Menezes, Mozart B.C. & da Silveira, Giovani J.C. & Drezner, Zvi, 2016. "Democratic elections and centralized decisions: Condorcet and Approval Voting compared with Median and Coverage locations," European Journal of Operational Research, Elsevier, vol. 253(1), pages 195-203.
    15. Wesley H. Holliday & Eric Pacuit, 2020. "Split Cycle: A New Condorcet Consistent Voting Method Independent of Clones and Immune to Spoilers," Papers 2004.02350, arXiv.org, revised Mar 2021.
    16. Eric Kamwa, 2021. "To what extent does the model of processing sincereincomplete rankings affect the likelihood of thetruncation paradox?," Working Papers hal-02879390, HAL.

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