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Arrow's Theorem for Economic Domains and Edgeworth Hyperboxes

Author

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  • Bordes, Georges
  • Campbell, Donald E
  • Le Breton, Michel

Abstract

Kenneth J. Arrow's theorem holds when the set of alternatives is an Edgeworth hyperbox and the individuals have classical economic preferences over their consumption sets. (Free disposability is not assumed.) By classical individual preferences the authors mean preorders satisfying continuity, strict convexity, strict monotonicity, and selfishness. A minor, but noteworthy, accomplishment is the development of a general technique for extending two-commodity impossibility theorems to the general m-commodity counterpart. Copyright 1995 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Suggested Citation

  • Bordes, Georges & Campbell, Donald E & Le Breton, Michel, 1995. "Arrow's Theorem for Economic Domains and Edgeworth Hyperboxes," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 36(2), pages 441-454, May.
    • Handle: RePEc:ier:iecrev:v:36:y:1995:i:2:p:441-54
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    Cited by:

    1. 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.
    2. Marc Fleurbaey & Alain Trannoy, 2003. "The impossibility of a Paretian egalitarian," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(2), pages 243-263, October.
    3. Walter Bossert & John A. Weymark, 2006. "Social Choice: Recent Developments," Vanderbilt University Department of Economics Working Papers 0603, Vanderbilt University Department of Economics.
    4. John Bone, "undated". "A simple version and extension of Arrow’s Theorem in the Edgeworth Domain," Discussion Papers 00/23, Department of Economics, University of York.
    5. Mridu Goswami, 2015. "Non fixed-price trading rules in single-crossing classical exchange economies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(2), pages 389-422, February.
    6. Sakai, Toyotaka, 2009. "Walrasian social orderings in exchange economies," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 16-22, January.
    7. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2020. "Arrow on domain conditions: a fruitful road to travel," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 237-258, March.
    8. Cato, Susumu, 2010. "Local strict envy-freeness in large economies," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 319-322, May.

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