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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 - Université de Yaoundé I [Yaoundé])

  • 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
    Note: View the original document on HAL open archive server: http://hal.univ-reunion.fr/hal-01697627
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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. Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2008. "On Ehrhart polynomials and probability calculations in voting theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 363-383, April.
    3. William Gehrlein & Dominique Lepelley & Issofa Moyouwou, 2015. "Voters’ preference diversity, concepts of agreement and Condorcet’s paradox," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(6), pages 2345-2368, November.
    4. 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.
    5. Gehrlein, William V., 1982. "Condorcet efficiency and constant scoring rules," Mathematical Social Sciences, Elsevier, vol. 2(2), pages 123-130, March.
    6. 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.
    7. William Gehrlein & Florenz Plassmann, 2014. "A comparison of theoretical and empirical evaluations of the Borda Compromise," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(3), pages 747-772, October.
    8. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    9. Alexander I. Barvinok, 1994. "A Polynomial Time Algorithm for Counting Integral Points in Polyhedra When the Dimension is Fixed," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 769-779, November.
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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, 2018. "Extensions of the Simpson voting rule to the committee selection setting," Working Papers 1813, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    3. 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.
    4. Mostapha Diss & Issofa Moyouwou & Hatem Smaoui & Eric Kamwa, 2020. "Condorcet efficiency of general weighted scoring rules under IAC: indifference and abstention," Post-Print hal-02196387, HAL.
    5. repec:spr:grdene:v:27:y:2018:i:4:d:10.1007_s10726-018-9580-z is not listed on IDEAS

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