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Nonbinary Social Choice: An Impossibility Theorem

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  • Grether, David M.
  • Plott, Charles R.

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.
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Suggested Citation

  • Grether, David M. & Plott, Charles R., "undated". "Nonbinary Social Choice: An Impossibility Theorem," Working Papers 271, California Institute of Technology, Division of the Humanities and Social Sciences.
  • Handle: RePEc:clt:sswopa:271
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    1. repec:spr:sochwe:v:48:y:2017:i:3:d:10.1007_s00355-017-1025-0 is not listed on IDEAS
    2. Campbell, Donald E. & Kelly, Jerry S., 1996. "Continuous-valued social choice," Journal of Mathematical Economics, Elsevier, vol. 25(2), pages 195-211.
    3. Dutta, Bhaskar & Jackson, Matthew O & Le Breton, Michel, 2001. "Strategic Candidacy and Voting Procedures," Econometrica, Econometric Society, vol. 69(4), pages 1013-1037, July.
    4. 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.
    5. 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.
    6. 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.
    7. Jeffrey Richelson, 1984. "Social choice and the status quo," Public Choice, Springer, vol. 42(3), pages 225-234, January.
    8. Geoffroy de Clippel, 2009. "Axiomatic Bargaining on Economic Enviornments with Lott," Working Papers 2009-5, Brown University, Department of Economics.
    9. repec:spr:grdene:v:23:y:2014:i:3:d:10.1007_s10726-013-9343-9 is not listed on IDEAS
    10. 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.
    11. Samejima, Yusuke, 2005. "Strategic candidacy, monotonicity, and strategy-proofness," Economics Letters, Elsevier, vol. 88(2), pages 190-195, August.
    12. Stefanescu, Anton, 1997. "Impossibility results for choice correspondences," Mathematical Social Sciences, Elsevier, vol. 33(2), pages 129-148, April.

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