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Monotonicity paradoxes in three-candidate elections using scoring elimination rules

Author

Listed:
  • Dominique Lepelley

    (CEMOI - Centre d'Économie et de Management de l'Océan Indien - UR - Université de La Réunion)

  • Issofa Moyouwou

    (MASS - UY1 - Université de Yaoundé I)

  • Hatem Smaoui

    (CEMOI - Centre d'Économie et de Management de l'Océan Indien - UR - Université de La Réunion)

Abstract

Scoring elimination rules (SER), that give points to candidates according to their rank in voters' preference orders and eliminate the candidate(s) with the lowest number of points, constitute an important class of voting rules. This class of rules, that includes some famous voting methods such as Plurality Runoff or Coombs Rule, suffers from a severe pathology known as monotonicity paradox or monotonicity failure, that is, getting more points from voters can make a candidate a loser and getting fewer points can make a candidate a winner. In this paper, we study three-candidate elections and we identify, under various conditions, which SER minimizes the probability that a monotonicity paradox occurs. We also analyze some strategic aspects of these monotonicity failures. The probability model on which our results are based is the impartial anonymous culture condition, often used in this kind of study.

Suggested Citation

  • Dominique Lepelley & Issofa Moyouwou & Hatem Smaoui, 2018. "Monotonicity paradoxes in three-candidate elections using scoring elimination rules," Post-Print hal-01697627, HAL.
    • Handle: RePEc:hal:journl:hal-01697627
    DOI: 10.1007/s00355-017-1069-1
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    Cited by:

    1. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2018. "The Chamberlin-Courant Rule and the k-Scoring Rules: Agreement and Condorcet Committee Consistency," Working Papers hal-01757761, HAL.
    2. Daniela Bubboloni & Mostapha Diss & Michele Gori, 2020. "Extensions of the Simpson voting rule to the committee selection setting," Public Choice, Springer, vol. 183(1), pages 151-185, April.
    3. Sylvain Béal & Marc Deschamps & Mostapha Diss & Issofa Moyouwou, 2022. "Inconsistent weighting in weighted voting games," Public Choice, Springer, vol. 191(1), pages 75-103, April.
    4. Mostapha Diss & Eric Kamwa & Issofa Moyouwou & Hatem Smaoui, 2019. "Condorcet efficiency of general weighted scoring rules under IAC: indifference and abstention," Working Papers hal-02196387, HAL.
    5. Barbaro, Salvatore, 2025. "Election methods and political polarization," Mathematical Social Sciences, Elsevier, vol. 135(C).
    6. Mostapha Diss & Eric Kamwa & Issofa Moyouwou & Hatem Smaoui, 2021. "Condorcet Efficiency of General Weighted Scoring Rules Under IAC: Indifference and Abstention," Studies in Choice and Welfare, in: Mostapha Diss & Vincent Merlin (ed.), Evaluating Voting Systems with Probability Models, pages 55-73, Springer.
    7. 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.
    8. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2025. "The effect of close elections on the likelihood of voting paradoxes: Further results in three-candidate elections," Post-Print hal-04230359, HAL.
    9. Dominique Lepelley & Hatem Smaoui, 2019. "Comparing Two Ways for Eliminating Candidates in Three-Alternative Elections Using Sequential Scoring Rules," Group Decision and Negotiation, Springer, vol. 28(4), pages 787-804, August.

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