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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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    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. repec:cup:apsrev:v:72:y:1978:i:04:p:1341-1356_15 is not listed on IDEAS
    3. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521808163, April.
    4. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521004046, March.
    5. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
    6. 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. 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. repec:kap:pubcho:v:173:y:2017:i:3:d:10.1007_s11127-017-0476-2 is not listed on IDEAS
    3. repec:spr:sochwe:v:50:y:2018:i:1:d:10.1007_s00355-017-1069-1 is not listed on IDEAS
    4. Jac C. Heckelman & Nicholas R. Miller (ed.), 2015. "Handbook of Social Choice and Voting," Books, Edward Elgar Publishing, number 15584, April.
    5. Marek M. Kaminski, 2015. "Empirical examples of voting paradoxes," Chapters,in: Handbook of Social Choice and Voting, chapter 20, pages 367-387 Edward Elgar Publishing.
    6. repec:eee:matsoc:v:89:y:2017:i:c:p:70-82 is not listed on IDEAS
    7. repec:kap:pubcho:v:173:y:2017:i:1:d:10.1007_s11127-017-0465-5 is not listed on IDEAS
    8. 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.

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