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The reinforcement axiom under sequential positional rules

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  • Sebastien Courtin

    (THEMA - Théorie économique, modélisation et applications - UCP - Université de Cergy Pontoise - Université Paris-Seine - CNRS - Centre National de la Recherche Scientifique)

  • Boniface Mbih

    (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)

  • Issofa Moyouwou

    (MASS - UY1 - Université de Yaoundé I)

  • Thomas Senné

    (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

The reinforcement axiom roughly states that when an alternative is selected by two different constituencies, it must also be selected by their union. Hare and Coombs rules are special cases of sequential positional voting rules, which are known to violate this axiom. In this article, we first show that reinforcement can be violated by all such rules. We then evaluate, by the use of Monte Carlo simulations and the Fishburn-Gehrlein technique, the proportion of profiles at which this phenomenon occurs.

Suggested Citation

  • Sebastien Courtin & Boniface Mbih & Issofa Moyouwou & Thomas Senné, 2010. "The reinforcement axiom under sequential positional rules," Post-Print hal-00914864, HAL.
    • Handle: RePEc:hal:journl:hal-00914864
    DOI: 10.1007/s00355-010-0449-6
    Note: View the original document on HAL open archive server: https://hal.science/hal-00914864
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    References listed on IDEAS

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    1. Boniface Mbih & Issofa Moyouwou & Xingyu Zhao, 2010. "On the positive association of parliamentary social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(1), pages 107-127, June.
    2. Dominique Lepelley, 1996. "Constant scoring rules, Condorcet criteria and single-peaked preferences (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(3), pages 491-500.
    3. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    4. Dominique Lepelley & Vincent Merlin, 2001. "Scoring run-off paradoxes for variable electorates," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 17(1), pages 53-80.
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    1. Sébastien Courtin & Boniface Mbih & Issofa Moyouwou, 2014. "Are Condorcet procedures so bad according to the reinforcement axiom?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 927-940, April.
    2. 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.

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    Keywords

    reinforcement axiom; scoring voting rules;

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