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Consistent collective decisions under majorities based on difference of votes

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  • Mostapha Diss

    (Université de Lyon, Lyon, F-69007, France ; CNRS, GATE Lyon St Etienne,F-69130 Ecully, France, Université Jean Monnet, Saint-Etienne, F-42000, France)

  • Patrizia Pérez-Asurmendi

    (Grupo de investigacion PRESAD, Universidad de Valladolid, Avda. Valle de Esgueva 6,47011, Valladolid, Spain & Grupo de investigacion SEED, Universidad Publica de Navarra, Campus de Arrosadia,31006, Pamplona, Spain.)

Abstract

The main criticism to the aggregation of individual preferences under majority rules refers to the possibility of reaching inconsistent collective decisions from the election process. In these cases, the collective preference includes cycles and even could prevent the election of any alternative as the collective choice. The likelihood of consistent outcomes under a class of majority rules constitutes the aim of this paper. Specifically, we focus on majority rules that require certain consensus in individual preferences to declare an alternative as the winner. Under majorities based on difference of votes, the requirement asks to the winner alternative to obtain a difference in votes with respect to the loser alternative taking into account that individuals are endowed with weak preference orderings. Same requirement is asked to the restriction of these rules to individual linear preferences.

Suggested Citation

  • Mostapha Diss & Patrizia Pérez-Asurmendi, 2015. "Consistent collective decisions under majorities based on difference of votes," Working Papers 1533, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    • Handle: RePEc:gat:wpaper:1533
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    References listed on IDEAS

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    1. Garcia-Lapresta, Jose Luis & Llamazares, Bonifacio, 2001. "Majority decisions based on difference of votes," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 463-481, June.
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    10. Balasko, Yves & Cres, Herve, 1997. "The Probability of Condorcet Cycles and Super Majority Rules," Journal of Economic Theory, Elsevier, vol. 75(2), pages 237-270, August.
    11. William Gehrlein & Peter Fishburn, 1983. "Scoring rule sensitivity to weight selection," Public Choice, Springer, vol. 40(3), pages 249-261, January.
    12. Tovey, Craig A., 1997. "Probabilities of Preferences and Cycles with Super Majority Rules," Journal of Economic Theory, Elsevier, vol. 75(2), pages 271-279, August.
    13. Lepelley, Dominique & Martin, Mathieu, 2001. "Condorcet's paradox for weak preference orderings," European Journal of Political Economy, Elsevier, vol. 17(1), pages 163-177, March.
    14. William Gehrlein & Peter Fishburn, 1981. "Constant scoring rules for choosing one among many alternatives," Quality & Quantity: International Journal of Methodology, Springer, vol. 15(2), pages 203-210, April.
    15. Llamazares, Bonifacio, 2006. "The forgotten decision rules: Majority rules based on difference of votes," Mathematical Social Sciences, Elsevier, vol. 51(3), pages 311-326, May.
    16. Llamazares, Bonifacio & Pérez-Asurmendi, Patrizia, 2013. "Triple-acyclicity in majorities based on difference in support," MPRA Paper 52218, University Library of Munich, Germany.
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    Cited by:

    1. Erik Friese & William V. Gehrlein & Dominique Lepelley & Achill Schürmann, 2017. "The impact of dependence among voters’ preferences with partial indifference," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(6), pages 2793-2812, November.
    2. Mostapha Diss & Patrizia Pérez-Asurmendi, 2016. "Probabilities of Consistent Election Outcomes with Majorities Based on Difference in Support," Group Decision and Negotiation, Springer, vol. 25(5), pages 967-994, September.

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    More about this item

    Keywords

    Majorities based on difference of votes; Probability; Transitivity; Triple-acyclicity.;
    All these keywords.

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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