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Scoring Run-off Rules, Single-peaked Preferences and Paradoxes of Variable Electorate

Author

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  • Eric Kamwa

    (LC2S - Laboratoire caribéen de sciences sociales - CNRS - Centre National de la Recherche Scientifique - UA - Université des Antilles, UA FDEM - Université des Antilles - Faculté de droit et d'économie de la Martinique - Université des Antilles (Pôle Martinique) - UA - Université des Antilles)

  • Vincent Merlin

    (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, CNRS - Centre National de la Recherche Scientifique, UNICAEN UFR SEGGAT - Université de Caen Normandie - UFR de Sciences Économiques, Gestion, Géographie et Aménagement des Territoires - UNICAEN - Université de Caen Normandie - NU - Normandie Université)

  • Faty Mbaye Top

    (INC - Institut National de la Consommation)

Abstract

This paper analyzes the vulnerability of scoring run-off rules to abstention and participation paradoxes when voters preferences are single-peaked. These paradoxes occur when the size of the electorate varies (grows or diminishes). In particular, the Abstention or No-show paradox occurs when a voter is better off by not casting his ballot in the election. First, we show that all the scoring run-off rules that always elect the Condorcet winner on this domain are immune to the different forms of Abstention and Participation paradoxes. Secondly, when these paradoxes are still possible, we compute their likelihood in three-candidate elections under the Impartial Anonymous Culture assumption. We conclude that considering the single-peaked domain drastically reduces, and even sometimes eliminates the impact of No-show paradoxes, for scoring run-off rules.

Suggested Citation

  • Eric Kamwa & Vincent Merlin & Faty Mbaye Top, 2023. "Scoring Run-off Rules, Single-peaked Preferences and Paradoxes of Variable Electorate," Working Papers hal-03143741, HAL.
    • Handle: RePEc:hal:wpaper:hal-03143741
    Note: View the original document on HAL open archive server: https://hal.science/hal-03143741v2
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    References listed on IDEAS

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    Keywords

    Paradoxes; Scoring Rules; Run-offs; No-show; Abstention; Participation; Impartial Anonymous Culture; Probability;
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