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


  • Florenz Plassmann


  • T. Tideman



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

    1. Marc Henry & Ismael Mourifié, 2013. "Euclidean Revealed Preferences: Testing The Spatial Voting Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(4), pages 650-666, June.
    2. Chamberlin, John R. & Cohen, Michael D., 1978. "Toward Applicable Social Choice Theory: A Comparison of Social Choice Functions under Spatial Model Assumptions," American Political Science Review, Cambridge University Press, vol. 72(4), pages 1341-1356, December.
    3. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521808163, December.
    4. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521004046, December.
    5. Jean-François Laslier, 2011. "And the loser is... Plurality Voting," Working Papers hal-00609810, HAL.
    6. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
    7. Dominique Lepelley & Vincent Merlin, 2001. "Scoring run-off paradoxes for variable electorates," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 17(1), pages 53-80.
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    Cited by:

    1. Conal Duddy, 2017. "Geometry of run-off elections," Public Choice, Springer, vol. 173(3), pages 267-288, December.
    2. repec:spr:sochwe:v:50:y:2018:i:1:d:10.1007_s00355-017-1069-1 is not listed on IDEAS
    3. Moyouwou, Issofa & Tchantcho, Hugue, 2017. "Asymptotic vulnerability of positional voting rules to coalitional manipulation," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 70-82.
    4. 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.
    5. 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.
    6. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2019. "On some k-scoring rules for committee elections: agreement and Condorcet Principle," Working Papers hal-02147735, HAL.
    7. repec:kap:theord:v:87:y:2019:i:3:d:10.1007_s11238-019-09716-5 is not listed on IDEAS
    8. 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.
    9. Jac C. Heckelman & Nicholas R. Miller (ed.), 2015. "Handbook of Social Choice and Voting," Books, Edward Elgar Publishing, number 15584, April.
    10. 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.
    11. 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.
    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.

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