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Borda elimination rule and monotonicity paradoxes in three-candidate elections

Author

Listed:
  • Hatem Smaoui

    (CEMOI University of La Réunion)

  • Dominique Lepelley

    (CEMOI University of La Réunion)

  • Issofa Moyouwou

    (Département de mathématiques - ENS - University of Yaoundé 1)

Abstract

We derive analytical representations for the vulnerability of Borda Elimination Rule (BER) to Monotonicity Paradoxes. These results allow to compare BER vulnerability with that of Plurality Elimination Rule (or Plurality Runoff) and Negative Plurality Elimination Rule (or Coombs Rule), that suffer from the same pathologies. We show that BER performs better than these two rules at avoiding 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

  • 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.
    • Handle: RePEc:ebl:ecbull:eb-16-00571
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    References listed on IDEAS

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    1. 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.
    2. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    3. 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.
    4. Wilson, Mark C. & Pritchard, Geoffrey, 2007. "Probability calculations under the IAC hypothesis," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 244-256, December.
    5. 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.
    6. 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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    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. 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.
    4. 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.
    5. Moyouwou, Issofa & Tchantcho, Hugue, 2017. "Asymptotic vulnerability of positional voting rules to coalitional manipulation," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 70-82.

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    More about this item

    Keywords

    Group decisions - Voting rules - Scoring Elimination Rules - Monotonicity failure;

    JEL classification:

    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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