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A Note on the Likelihood of the Absolute Majority Paradoxes

Author

Listed:
  • Mostapha Diss

    (Univ Lyon, UJM Saint-Etienne, GATE UMR 5824, F-42023 Saint-Etienne, France.)

  • Eric Kamwa

    (Université des Antilles, LC2S UMR CNRS 8053, F-97275 Schoelcher Cedex, France)

  • Abdelmonaim Tlidi

    (University Cadi Ayyad of Marrakesh, GREER, National School of Applied Science, Safi , Morocco)

Abstract

For three-candidate elections, we compute under the Impartial Anonymous Culture assumption, the conditional probabilities of the Absolute Majority Winner Paradox (AMWP) and the Absolute Majority Loser Paradox (AMLP) under the Plurality rule, the Borda rule, and the Negative Plurality rule for a given number of voters. We also provide a representation of the conditional probability of these paradoxes for the whole family of weighted scoring rules with large electorates. The AMWP occurs when a candidate who is ranked first by more than half of the voters is not selected by a given voting rule; the AMLP appears when a candidate who is ranked last by more than half of the voters is elected. As no research papers have tried to evaluate the likelihood of these paradoxes, this note is designed to fill this void. Our results allow us to claim that ignoring these two paradoxes in the literature, particularly AMWP, is not justified.

Suggested Citation

  • Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2018. "A Note on the Likelihood of the Absolute Majority Paradoxes," Economics Bulletin, AccessEcon, vol. 38(4), pages 1727-1734.
    • Handle: RePEc:ebl:ecbull:eb-18-00656
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    References listed on IDEAS

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    1. Diss, Mostapha & Louichi, Ahmed & Merlin, Vincent & Smaoui, Hatem, 2012. "An example of probability computations under the IAC assumption: The stability of scoring rules," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 57-66.
    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. Davide Cervone & William Gehrlein & William Zwicker, 2005. "Which Scoring Rule Maximizes Condorcet Efficiency Under Iac?," Theory and Decision, Springer, vol. 58(2), pages 145-185, March.
    5. William Gehrlein & Peter Fishburn, 1976. "Condorcet's paradox and anonymous preference profiles," Public Choice, Springer, vol. 26(1), pages 1-18, June.
    6. Mostapha Diss & William Gehrlein, 2012. "Borda’s Paradox with weighted scoring rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(1), pages 121-136, January.
    7. Mostapha Diss & William V. Gehrlein, 2015. "The True Impact of Voting Rule Selection on Condorcet Efficiency," Economics Bulletin, AccessEcon, vol. 35(4), pages 2418-2426.
    8. William V. Gehrlein & Dominique Lepelley, 2011. "Voting Paradoxes and Group Coherence," Studies in Choice and Welfare, Springer, number 978-3-642-03107-6, June.
    9. Eric Kamwa & Fabrice Valognes, 2017. "Scoring Rules and Preference Restrictions: The Strong Borda Paradox Revisited," Revue d'économie politique, Dalloz, vol. 127(3), pages 375-395.
    10. Kuga, Kiyoshi & Nagatani, Hiroaki, 1974. "Voter Antagonism and the Paradox of Voting," Econometrica, Econometric Society, vol. 42(6), pages 1045-1067, November.
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    Citations

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    Cited by:

    1. 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.
    2. Fabrice Barthelemy & Dominique Lepelley & Mathieu Martin & Hatem Smaoui, 2021. "Dummy Players and the Quota in Weighted Voting Games," Group Decision and Negotiation, Springer, vol. 30(1), pages 43-61, February.
    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. Eric Kamwa, 2019. "On the Likelihood of the Borda Effect: The Overall Probabilities for General Weighted Scoring Rules and Scoring Runoff Rules," Group Decision and Negotiation, Springer, vol. 28(3), pages 519-541, June.
    5. Eric Kamwa, 2022. "Scoring rules, ballot truncation, and the truncation paradox," Public Choice, Springer, vol. 192(1), pages 79-97, July.
    6. Abdelhalim El Ouafdi & Dominique Lepelley & Hatem Smaoui, 2020. "Probabilities of electoral outcomes: from three-candidate to four-candidate elections," Theory and Decision, Springer, vol. 88(2), pages 205-229, March.
    7. Eric Kamwa, 2022. "Scoring Rules, Ballot Truncation, and the Truncation Paradox," Working Papers hal-03632662, HAL.
    8. Ahmad Awde & Mostapha Diss & Eric Kamwa & Julien Yves Rolland & Abdelmonaim Tlidi, 2022. "Social unacceptability for simple voting procedures," Working Papers hal-03614587, HAL.
    9. Aleksei Y. Kondratev & Alexander S. Nesterov, 2020. "Measuring majority power and veto power of voting rules," Public Choice, Springer, vol. 183(1), pages 187-210, April.
    10. Eric Kamwa, 2019. "Condorcet efficiency of the preference approval voting and the probability of selecting the Condorcet loser," Theory and Decision, Springer, vol. 87(3), pages 299-320, October.
    11. Jac C. Heckelman, 2021. "Characterizing plurality using the majoritarian condition: a new proof and implications for other scoring rules," Public Choice, Springer, vol. 189(3), pages 335-346, December.
    12. Eric Kamwa, 2021. "To what extent does the model of processing sincereincomplete rankings affect the likelihood of the truncation paradox?," Working Papers hal-02879390, HAL.

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    More about this item

    Keywords

    Ranking; Scoring rule; Paradox; Majority; IAC;
    All these keywords.

    JEL classification:

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

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