A representative individual from Arrovian aggregation of parametric individual utilities

Frederik Herzberg

No 411, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: 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.

Keywords: Ultraproduct; Nonstandard analysis; Ultrafilter; Arrovian social choice; Representative individual (search for similar items in EconPapers)
Date: 2011-08-16
New Economics Papers: this item is included in nep-cdm and nep-upt
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https://pub.uni-bielefeld.de/download/2316447/2319870 First Version, 2009 (application/pdf)

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Journal Article: A representative individual from Arrovian aggregation of parametric individual utilities (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:411

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