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On the Likelihood of the Borda Effect: The Overall Probabilities for General Weighted Scoring Rules and Scoring Runoff Rules

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  • Eric Kamwa

    (LC2S UMR CNRS 8053 and Université des Antilles)

Abstract

The Borda Effect, first introduced by Colman and Poutney (Behav Sci 23:15–20, 1978), occurs in a preference aggregation process using the Plurality rule if given the (unique) winner there is at least one loser that is preferred to the winner by a majority of the electorate. Colman and Poutney (1978) distinguished two forms of the Borda Effect: the Weak Borda Effect, describing a situation under which the unique winner of the Plurality rule is majority dominated by only one loser; and the Strong Borda Effect, under which the Plurality winner is majority dominated by each of the losers. The Strong Borda Effect is well documented in the literature as the Strong Borda Paradox. Colman and Poutney (1978) showed that the probability of the Weak Borda Effect is not negligible; but they only focused on the Plurality rule. In this note, we extend the work of Colman and Poutney (1978) by providing, for three-candidate elections, representations of the limiting probabilities of the (Weak) Borda Effect for the whole family of scoring rules and scoring runoff rules. Our analysis leads us to highlight that there is a relation between the (Weak) Borda Effect and Condorcet efficiency. We perform our analysis under the assumptions of Impartial Culture and Impartial Anonymous Culture, which are two well-known assumptions often used for such a study.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:grdene:v:28:y:2019:i:3:d:10.1007_s10726-018-9605-7
    DOI: 10.1007/s10726-018-9605-7
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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 & 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.
    3. 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.
    4. 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.
    5. Eric Kamwa & Issofa Moyouwou, 2021. "Susceptibility to Manipulation by Sincere Truncation: The Case of Scoring Rules and Scoring Runoff Systems," Studies in Choice and Welfare, in: Mostapha Diss & Vincent Merlin (ed.), Evaluating Voting Systems with Probability Models, pages 275-295, Springer.
    6. 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.
    7. 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.
    8. 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.
    9. Eric Kamwa & Issofa Moyouwou, 2019. "Susceptibility to Manipulation by Sincere Truncation : the Case of Scoring Rules and Scoring Runoff Systems," Working Papers hal-02185965, HAL.
    10. Eric Kamwa, 2022. "Scoring Rules, Ballot Truncation, and the Truncation Paradox," Working Papers hal-03632662, HAL.

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