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Nonbinary Social Choice: An Impossibility Theorem

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  • David M. Grether
  • Charles R. Plott

Abstract

This paper contains a generalization of the General Possibility Theorem to situations where choice over two-element (more generally, "small") sets is not possible. The analysis is developed in terms of the social choice function formulation rather than the social welfare function approach. In this formulation, assumptions concerning the size of sets of feasible alternatives are explicit, allowing the role of these assumptions in inducing impossibility results to be explored.

Suggested Citation

  • David M. Grether & Charles R. Plott, 1982. "Nonbinary Social Choice: An Impossibility Theorem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(1), pages 143-149.
    • Handle: RePEc:oup:restud:v:49:y:1982:i:1:p:143-149.
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    File URL: http://hdl.handle.net/10.2307/2297147
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    Cited by:

    1. Shino Takayama & Akira Yokotani, 2017. "Social choice correspondences with infinitely many agents: serial dictatorship," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 573-598, March.
    2. Campbell, Donald E. & Kelly, Jerry S., 1996. "Continuous-valued social choice," Journal of Mathematical Economics, Elsevier, vol. 25(2), pages 195-211.
    3. de Clippel, Geoffroy & Bejan, Camelia, 2011. "No profitable decompositions in quasi-linear allocation problems," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1995-2012, September.
    4. Le Breton, Michel & Weymark, John A., 2002. "Arrovian Social Choice Theory on Economic Domains," IDEI Working Papers 143, Institut d'Économie Industrielle (IDEI), Toulouse, revised Sep 2003.
    5. Susumu Cato, 2014. "Menu Dependence and Group Decision Making," Group Decision and Negotiation, Springer, vol. 23(3), pages 561-577, May.
    6. SAKAMOTO, Norihito & 坂本, 徳仁 & TADENUMA, Koichi & 蓼沼, 宏一, 2024. "Independent Decisiveness, Dictatorship, and Inter-menu Consistency," Discussion Papers 2024-03, Graduate School of Economics, Hitotsubashi University.
    7. Lars Ehlers & John A. Weymark, 2003. "Candidate stability and nonbinary social choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(2), pages 233-243, September.
    8. Dutta, Bhaskar & Jackson, Matthew O & Le Breton, Michel, 2001. "Strategic Candidacy and Voting Procedures," Econometrica, Econometric Society, vol. 69(4), pages 1013-1037, July.
    9. Susumu Cato, 2018. "Collective rationality and decisiveness coherence," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(2), pages 305-328, February.
    10. Priscilla Man & Shino Takayama, 2013. "A unifying impossibility theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 249-271, October.
    11. Jeffrey Richelson, 1984. "Social choice and the status quo," Public Choice, Springer, vol. 42(3), pages 225-234, January.
    12. Geoffroy de Clippel, 2009. "Axiomatic Bargaining on Economic Enviornments with Lott," Working Papers 2009-5, Brown University, Department of Economics.
    13. Samejima, Yusuke, 2005. "Strategic candidacy, monotonicity, and strategy-proofness," Economics Letters, Elsevier, vol. 88(2), pages 190-195, August.
    14. Donald Campbell & Jerry Kelly, 2013. "Relaxing IIA and the effect on individual power," Review of Economic Design, Springer;Society for Economic Design, vol. 17(3), pages 165-181, September.
    15. Ning Yu, 2015. "A quest for fundamental theorems of social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 533-548, March.
    16. Stefanescu, Anton, 1997. "Impossibility results for choice correspondences," Mathematical Social Sciences, Elsevier, vol. 33(2), pages 129-148, April.

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