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Scoring Rules and Preference Restrictions: The Strong Borda Paradox Revisited

Author

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  • Eric Kamwa

    (LC2S - Laboratoire caribéen de sciences sociales - CNRS - Centre National de la Recherche Scientifique - UA - Université des Antilles)

  • Fabrice Valognes

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

Abstract

For a given voting situation, the Strong Borda Paradox occurs when a Condorcet loser exists and is elected. A Condorcet loser is a candidate that loses all his pairwise comparisons. In three-candidate elections, we use an analytical approach to find out, the range of all the scoring rules that can exhibit the Strong Borda Paradox under some well-known preference restrictions and we describe all the scenarios with respect to the rank of the Condorcet loser in the collective rankings. Using the parameterized Barvinok's algorithm, we provide a simplified representation of the likelihood of the Strong Borda Paradox for the Plurality rule and the Antiplurality rule (given the size of the electorate) with the impartial and anonymous culture condition for each type of restriction.

Suggested Citation

  • Eric Kamwa & Fabrice Valognes, 2017. "Scoring Rules and Preference Restrictions: The Strong Borda Paradox Revisited," Post-Print hal-01631180, HAL.
    • Handle: RePEc:hal:journl:hal-01631180
    DOI: 10.3917/redp.273.0375
    Note: View the original document on HAL open archive server: https://hal.univ-antilles.fr/hal-01631180
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    Cited by:

    1. Eric Kamwa, 2022. "Scoring rules, ballot truncation, and the truncation paradox," Public Choice, Springer, vol. 192(1), pages 79-97, July.
    2. Mostapha Diss & Abdelmonaim Tlidi, 2018. "Another perspective on Borda’s paradox," Theory and Decision, Springer, vol. 84(1), pages 99-121, January.
    3. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2020. "On Some k -scoring Rules for Committee Elections: Agreement and Condorcet Principle," Revue d'économie politique, Dalloz, vol. 130(5), pages 699-725.
    4. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2019. "On some k-scoring rules for committee elections: agreement and Condorcet Principle," Working Papers hal-02147735, HAL.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Eric Kamwa, 2022. "Scoring Rules, Ballot Truncation, and the Truncation Paradox," Working Papers hal-03632662, HAL.

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