A representative individual from Arrovian aggregation of parametric individual utilities
AbstractAbstract This article investigates the representative-agent hypothesis for a population which faces a collective choice from a given finite-dimensional space of alternatives. Each individual's preference ordering is assumed to admit a utility representation through an element of an exogenously given set of admissible utility functions. In addition, we assume that (i) the class of admissible utility functions allows for a smooth parametrization and only consists of strictly concave functions, (ii) the population is infinite, and (iii) 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. Given the structural similarities among the admissible utility functions (due to parametrization), we argue that the representative utility function can be interpreted as belonging to an - actual or invisible- individual. The existence proof for the representative utility function utilizes a special nonstandard model of the reals, viz. the ultrapower of the reals with respect to the ultrafilter of decisive coalitions; this construction explicitly determines the parameter vector of the representative utility function.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 46 (2010)
Issue (Month): 6 (November)
Contact details of provider:
Web page: http://www.elsevier.com/locate/jmateco
Representative individual Arrovian social choice Ultrafilter Ultraproduct Nonstandard analysis;
Other versions of this item:
- Frederik Herzberg, 2009. "A representative individual from Arrovian aggregation of parametric individual utilities," Working Papers 411, Bielefeld University, Center for Mathematical Economics.
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Campbell, Donald E., 1990. "Intergenerational social choice without the Pareto principle," Journal of Economic Theory, Elsevier, vol. 50(2), pages 414-423, April.
- 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.
- Herzberg, Frederik & Lauwers, Luc & Van Liedekerke, Luc & Senyo, Emmanuel, 2010.
"Ultraproducts and aggregation,"
Open Access publications from Katholieke Universiteit Leuven
urn:hdl:123456789/258870, Katholieke Universiteit Leuven.
- 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.
- Sen, Amartya, 1995. "Rationality and Social Choice," American Economic Review, American Economic Association, vol. 85(1), pages 1-24, March.
- 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.
- Schmitz, Norbert, 1977. "A further note on arrow's impossibility theorem," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 189-196, August.
- Clark, Stephen A., 1992. "The representative agent model of probabilistic social choice," Mathematical Social Sciences, Elsevier, vol. 23(1), pages 45-66, February.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wendy Shamier).
If references are entirely missing, you can add them using this form.