A representative individual from arrovian aggregation of parametric individual utilities

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Working Papers ; No. 411

Classification and Topics

• Classification: Wirtschaft ; Social Choice; Clubs; Committees; Associations
• Subject: Representative individual ; Arrovian social choice ; Ultrafilter ; Ultraproduct ; Nonstandard analysis ; Nutzenfunktion ; Aggregation ; Soziale Wohlfahrtsfunktion ; Unmöglichkeitstheorem ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Herzberg, Frederik
• Event: Veröffentlichung
• (who): Bielefeld University, Institute of Mathematical Economics (IMW)
• (where): Bielefeld
• (when): 2009

Further information

• Handle: http://hdl.handle.net/10419/43804
• URN: urn:nbn:de:hbz:361-14457
• Last update: 10.03.2025, 11:44 AM CET