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A representative individual from Arrovian aggregation of parametric individual utilities

  • Frederik Herzberg

    ()

    (Institute of Mathematical Economics, Bielefeld University)

This article investigates the representative-agent hypothesis for an infinite population which has to make a social choice from a given finite-dimensional space of alternatives. It is assumed that some class of admissible strictly concave utility functions is exogenously given and that each individual's preference ordering can be represented cardinally through some admissible utility function. In addition, we assume that (i) the class of admissible utility functions allows for a smooth parametrization, and (ii) the social welfare function satisfies Arrovian rationality axioms. We prove that there exists an admissible utility function r, called representative utility function, such that any alternative which maximizes r also maximizes the social welfare function. The proof utilizes a special nonstandard model of the reals, viz. the ultraproduct of the reals with respect to the ultrafilter of decisive coalitions; this construction explicitly determines the parameter vector of the representative utility function.

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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-411.pdf
File Function: First version, 2009
Download Restriction: no

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 411.

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Length: 17 pages
Date of creation: Jan 2009
Date of revision:
Handle: RePEc:bie:wpaper:411
Contact details of provider: Postal: Postfach 10 01 31, 33501 Bielefeld
Phone: +49(0)521-106-4907
Web page: http://www.imw.uni-bielefeld.de/

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  1. James E. Hartley, 1996. "Retrospectives: The Origins of the Representative Agent," Journal of Economic Perspectives, American Economic Association, vol. 10(2), pages 169-177, Spring.
  2. Alan P. Kirman, 1992. "Whom or What Does the Representative Individual Represent?," Journal of Economic Perspectives, American Economic Association, vol. 6(2), pages 117-136, Spring.
  3. Anderson, Robert M., 1991. "Non-standard analysis with applications to economics," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 39, pages 2145-2208 Elsevier.
  4. Campbell, Donald E., 1990. "Intergenerational social choice without the Pareto principle," Journal of Economic Theory, Elsevier, vol. 50(2), pages 414-423, April.
  5. Lauwers, Luc & Van Liedekerke, Luc, 1995. "Ultraproducts and aggregation," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 217-237.
  6. Schmitz, Norbert, 1977. "A further note on arrow's impossibility theorem," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 189-196, August.
  7. Clark, Stephen A., 1992. "The representative agent model of probabilistic social choice," Mathematical Social Sciences, Elsevier, vol. 23(1), pages 45-66, February.
  8. Sen, Amartya, 1995. "Rationality and Social Choice," American Economic Review, American Economic Association, vol. 85(1), pages 1-24, March.
  9. Grafe, F. & Grafe, J., 1983. "On arrow-type impossibility theorems with infinite individuals and infinite alternatives," Economics Letters, Elsevier, vol. 11(1-2), pages 75-79.
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