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Title:A representative individual from arrovian aggregation of parametric individual utilities PDF Logo
Authors:Herzberg, Frederik
Issue Date:2009
Series/Report no.:Working papers // Institute of Mathematical Economics 411
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.
Subjects:Representative individual
Arrovian social choice
Ultrafilter
Ultraproduct
Nonstandard analysis
JEL:D71
Persistent Identifier of the first edition:urn:nbn:de:hbz:361-14457
Document Type:Working Paper
Appears in Collections:Working Papers, Institute of Mathematical Economics, Universität Bielefeld

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