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Triple-acyclicity in majorities based on difference in support

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  • Llamazares, Bonifacio
  • Pérez-Asurmendi, Patrizia

Abstract

In this paper we study to what extent majorities based on difference in support leads to triple-acyclic collective decisions. These majorities, which take into account voters' intensities of preference between pairs of alternatives through reciprocal preference relations, require to the winner alternative to exceed the support for the other alternative in a difference fixed before the election. Depending on that difference, i.e., on the threshold of support, and on some requirements on the individual rationality of the voters, we provide necessary and sufficient conditions for avoiding cycles of three alternatives on the collective decision.

Suggested Citation

  • Llamazares, Bonifacio & Pérez-Asurmendi, Patrizia, 2013. "Triple-acyclicity in majorities based on difference in support," MPRA Paper 52218, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:52218
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    File URL: https://mpra.ub.uni-muenchen.de/52218/1/MPRA_paper_52218.pdf
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    References listed on IDEAS

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    1. Herrera-Viedma, E. & Herrera, F. & Chiclana, F. & Luque, M., 2004. "Some issues on consistency of fuzzy preference relations," European Journal of Operational Research, Elsevier, vol. 154(1), pages 98-109, April.
    2. 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.
    3. Houy, Nicolas, 2007. "Some further characterizations for the forgotten voting rules," Mathematical Social Sciences, Elsevier, vol. 53(1), pages 111-121, January.
    4. B. Baets & H. Meyer & B. Schuymer, 2006. "Cyclic Evaluation of Transitivity of Reciprocal Relations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 217-238, April.
    5. Llamazares, Bonifacio, 2004. "Simple and absolute special majorities generated by OWA operators," European Journal of Operational Research, Elsevier, vol. 158(3), pages 707-720, November.
    6. Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
    7. José Luis Garcí a-Lapresta & Bonifacio Llamazares, 2010. "Preference Intensities and Majority Decisions Based on Difference of Support Between Alternatives," Group Decision and Negotiation, Springer, vol. 19(6), pages 527-542, November.
    8. Susumu Cato & Daisuke Hirata, 2010. "Collective choice rules and collective rationality: a unified method of characterizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(4), pages 611-630, April.
    9. Rajat Deb & Manabendra Dasgupta, 1996. "Transitivity and fuzzy preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(3), pages 305-318.
    10. JosÊ Luis GarcÎa-Lapresta & Bonifacio Llamazares, 2000. "Aggregation of fuzzy preferences: Some rules of the mean," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(4), pages 673-690.
    11. 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.
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    Cited by:

    1. Mostapha Diss & Patrizia Pérez-Asurmendi, 2016. "Consistent collective decisions under majorities based on difference of votes," Theory and Decision, Springer, vol. 80(3), pages 473-494, March.
    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.
    3. Mostapha Diss & Patrizia Pérez-Asurmendi, 2015. "Consistent collective decisions under majorities based on difference of votes," Working Papers halshs-01241996, HAL.

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    More about this item

    Keywords

    Triple-acyclicity; Majorities based on difference in support; Reciprocal preference relations; Voting systems.;
    All these keywords.

    JEL classification:

    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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