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Unifying voting theory from Nakamura’s to Greenberg’s theorems

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  • Saari, Donald G.

Abstract

Cycles, empty cores, intransitivities, and other complexities affect group decision and voting rules. Approaches that prevent these difficulties include the Nakamura number, Greenberg’s theorem, and single peaked preferences. The results derived here subsume and significantly extend these assertions while providing a common explanation for these seemingly dissimilar conclusions.

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  • Saari, Donald G., 2014. "Unifying voting theory from Nakamura’s to Greenberg’s theorems," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 1-11.
    • Handle: RePEc:eee:matsoc:v:69:y:2014:i:c:p:1-11
    DOI: 10.1016/j.mathsocsci.2014.01.001
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    9. Donald G. Saari, 1997. "The generic existence of a core for q -rules (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 219-260.
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    Cited by:

    1. Mathieu Martin & Zéphirin Nganmeni & Craig A. Tovey, 2019. "Dominance in Spatial Voting with Imprecise Ideals: A New Characterization of the Yolk," THEMA Working Papers 2019-02, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    2. Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean‐Baptiste Tondji, 2022. "Vaccine and inclusion," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 1101-1123, October.
      • Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean-Baptiste Tondji, 2022. "Vaccine and Inclusion," Working Papers 2202E Classification-C62,, University of Ottawa, Department of Economics.
    3. Mathieu Martin & Zéphirin Nganmeni, 2019. "The fi nagle point might not be within the Ɛ-core: a contradiction with Bräuninger's result," THEMA Working Papers 2019-03, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    4. Josep Freixas & Sascha Kurz, 2019. "Bounds for the Nakamura number," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(4), pages 607-634, April.
    5. Mathieu Martin & Zéphirin Nganmeni & Craig A. Tovey, 2021. "Dominance in spatial voting with imprecise ideals," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 181-195, July.
    6. Mostapha Diss & Michele Gori, 2022. "Majority properties of positional social preference correspondences," Theory and Decision, Springer, vol. 92(2), pages 319-347, March.
    7. Donald G. Saari, 2019. "Arrow, and unexpected consequences of his theorem," Public Choice, Springer, vol. 179(1), pages 133-144, April.
    8. McIntee, Tomas J. & Saari, Donald G., 2017. "Likelihood of voting outcomes with generalized IAC probabilities," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 1-10.

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