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Monotonicity Violations by Borda’s Elimination and Nanson’s Rules: A Comparison

Author

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  • Dan S. Felsenthal

    (University of Haifa)

  • Hannu Nurmi

    (University of Turku)

Abstract

This paper compares the vulnerability of Borda Elimination Rule (BER) and of Nanson Elimination Rule (NER) to monotonicity paradoxes under both fixed and variable electorates. It is shown that while NER is totally immune and BER is vulnerable to monotonicity failure in 3-candidate elections, neither of these two rules dominates the other in n-candidate elections (n > 3) when no Condorcet Winner exists. When the number of competing alternatives is larger than three and no Condorcet Winner exists, we find profiles where NER violates monotonicity while BER does not, profiles where BER violates monotonicity while NER does not, as well as profiles where both NER and BER violate monotonicity. These findings extend to both fixed and variable electorates, as well as to situations where the initial winners under both rules are the same, as well as to situations where the initial winners under both rules are different. So, which of the two rules should be preferred in terms of monotonicity in n-candidate elections (n > 3) where no Condorcet Winner exists, depends on the kind of profiles one can expect to encounter in practice most often. Nevertheless, in view of the results of 3-candidate elections under other scoring elimination rules, we conjecture that inasmuch as BER and NER exhibit monotonicity failures, it is more likely to occur in closely contested elections.

Suggested Citation

  • Dan S. Felsenthal & Hannu Nurmi, 2018. "Monotonicity Violations by Borda’s Elimination and Nanson’s Rules: A Comparison," Group Decision and Negotiation, Springer, vol. 27(4), pages 637-664, August.
    • Handle: RePEc:spr:grdene:v:27:y:2018:i:4:d:10.1007_s10726-018-9580-z
    DOI: 10.1007/s10726-018-9580-z
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    References listed on IDEAS

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    1. Hatem Smaoui & Dominique Lepelley & Issofa Moyouwou, 2016. "Borda elimination rule and monotonicity paradoxes in three-candidate elections," Economics Bulletin, AccessEcon, vol. 36(3), pages 1722-1728.
    2. Emerson Niou, 1987. "A note on Nanson's rule," Public Choice, Springer, vol. 54(2), pages 191-193, January.
    3. James Green-Armytage & T. Tideman & Rafael Cosman, 2016. "Statistical evaluation of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 183-212, January.
    4. Dan S. Felsenthal, 2012. "Review of Paradoxes Afflicting Procedures for Electing a Single Candidate," Studies in Choice and Welfare, in: Dan S. Felsenthal & Moshé Machover (ed.), Electoral Systems, chapter 0, pages 19-91, Springer.
    5. Mostapha Diss & Ahmed Doghmi, 2016. "Multi-winner scoring election methods: Condorcet consistency and paradoxes," Public Choice, Springer, vol. 169(1), pages 97-116, October.
    6. 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.
    7. Lepelley, Dominique & Chantreuil, Frederic & Berg, Sven, 1996. "The likelihood of monotonicity paradoxes in run-off elections," Mathematical Social Sciences, Elsevier, vol. 31(3), pages 133-146, June.
    8. Nicholas R. Miller, 2017. "Closeness matters: monotonicity failure in IRV elections with three candidates," Public Choice, Springer, vol. 173(1), pages 91-108, October.
    9. Dan S. Felsenthal & Hannu Nurmi, 2017. "Monotonicity Failures Afflicting Procedures for Electing a Single Candidate," SpringerBriefs in Economics, Springer, number 978-3-319-51061-3, October.
    10. Dan S. Felsenthal & Hannu Nurmi, 2016. "Two types of participation failure under nine voting methods in variable electorates," Public Choice, Springer, vol. 168(1), pages 115-135, July.
    11. Gehrlein, William V., 2001. "Condorcet winners on four candidates with anonymous voters," Economics Letters, Elsevier, vol. 71(3), pages 335-340, June.
    12. 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.
    13. Dan Felsenthal & Nicolaus Tideman, 2013. "Varieties of failure of monotonicity and participation under five voting methods," Theory and Decision, Springer, vol. 75(1), pages 59-77, July.
    14. William V. Gehrlein & Dominique Lepelley, 2011. "Voting paradoxes and group coherence: the condorcet efficiency of voting rules," Post-Print hal-01243452, HAL.
    15. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    16. Moulin, Herve, 1988. "Condorcet's principle implies the no show paradox," Journal of Economic Theory, Elsevier, vol. 45(1), pages 53-64, June.
    17. William V. Gehrlein & Dominique Lepelley, 2011. "Voting Paradoxes and Group Coherence," Studies in Choice and Welfare, Springer, number 978-3-642-03107-6, June.
    18. Felsenthal, Dan S. & Tideman, Nicolaus, 2014. "Interacting double monotonicity failure with direction of impact under five voting methods," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 57-66.
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