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Multi-dimensional rules

Author

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  • Sebastien Courtin

    (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)

  • Annick Laruelle

    (Ikerbasque - Basque Foundation for Science)

Abstract

Highlights The decision structures aggregate the opinions of voters on several dimensions. Characterization of weighted multi-dimensional rules is provided. Some multi-dimensional rules are represented by a combination of single dimension rules. Links to the referendum paradox and the Ostrogorski paradox are made.AbstractThis paper deals with rules that specify the collective acceptance or rejection of a proposal with several dimensions. We introduce the notions of separability and weightedness in this context. We provide a partial characterization of separable rules and show the independence between separability and weightedness.

Suggested Citation

  • Sebastien Courtin & Annick Laruelle, 2020. "Multi-dimensional rules," Post-Print hal-02351433, HAL.
    • Handle: RePEc:hal:journl:hal-02351433
    DOI: 10.1016/j.mathsocsci.2019.10.001
    Note: View the original document on HAL open archive server: https://hal.science/hal-02351433
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    References listed on IDEAS

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    1. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638, September.
    2. Dominique Lepelley & N. Andjiga & F. Chantreuil, 2003. "La mesure du pouvoir de vote," Post-Print halshs-00069255, HAL.
    3. Laffond, Gilbert & Laine, Jean, 2000. "Representation in majority tournaments," Mathematical Social Sciences, Elsevier, vol. 39(1), pages 35-53, January.
    4. Marc Feix & Dominique Lepelley & Vincent Merlin & Jean-Louis Rouet, 2004. "The probability of conflicts in a U.S. presidential type election," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(2), pages 227-257, January.
    5. Anand, Paul & Pattanaik, Prasanta & Puppe, Clemens (ed.), 2009. "The Handbook of Rational and Social Choice," OUP Catalogue, Oxford University Press, number 9780199290420.
    6. Deb, Rajat & Kelsey, David, 1987. "On constructing a generalized ostrogorski paradox: Necessary and sufficient conditions," Mathematical Social Sciences, Elsevier, vol. 14(2), pages 161-174, October.
    7. Annick Laruelle & Federico Valenciano, 2012. "Quaternary dichotomous voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 431-454, March.
    8. Laffond, G. & Laine, J., 2006. "Single-switch preferences and the Ostrogorski paradox," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 49-66, July.
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    Cited by:

    1. Courtin, Sébastien, 2022. "Evaluation of decision power in multi-dimensional rules," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 27-36.

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