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Title:   A representative individual from arrovian aggregation of parametric individual utilities 
Authors:   Herzberg, Frederik 
Issue Date:   2009 
Series/Report no.:   Working papers // Institute of Mathematical Economics 411 
Abstract:   This article investigates the representativeagent hypothesis for an infinite population which has to make a social choice from a given finitedimensional 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:36114457 
Document Type:   Working Paper 
Appears in Collections:   Working Papers, Center for Mathematical Economics (IMW), Bielefeld University

 

 
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