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Social choice of convex risk measures through Arrovian aggregation of variational preferences

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  • Frederik Herzberg

    (Institute of Mathematical Economics, Bielefeld University)

Abstract

It is known that a combination of the Maccheroni-Marinacci-Rustichini (2006) axiomatisation of variational preferences with the Föllmer-Schied (2002,2004) representation theorem for concave monetary utility functionals provides an (individual) decision-theoretic foundation for convex risk measures. The present paper is devoted to collective decision making with regard to convex risk measures and addresses the existence problem for non-dictatorial aggregation functions of convex risk measures - in the guise of variational preferences - satisfying Arrow-type rationality axioms (weak universality, systematicity, Pareto principle). We prove an impossibility result for finite electorates, viz. a variational analogue of Arrow's impossibility theorem. For infinite electorates, the possibility of rational aggregation of variational preferences (i.e. convex risk measures) depends on a uniform continuity condition for the variational preference profiles: We shall prove variational analogues of both Campbell's impossibility theorem and Fishburn's possibility theorem. Methodologically, we adopt the model-theoretic approach to aggregation theory inspired by Lauwers-Van Liedekerke (1995). In an appendix, we apply the Dietrich-List (2010) analysis of logical aggregation based on majority voting to the problem of variational preference aggregation. The fruit is a possibility theorem, but at the cost of considerable and - at least at first sight - rather unnatural restrictions on the domain of the variational preference aggregator.

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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-432.pdf
File Function: First version, 2010
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Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 432.

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Length: 16 pages
Date of creation: May 2010
Date of revision:
Handle: RePEc:bie:wpaper:432

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Related research

Keywords: variational preference representation; convex risk measure; multiple priors preferences; Arrow-type preference aggregation; judgment aggregation; abstract aggregation theory; model theory; first-order predicate logic; ultrafilter; ultraproduct;

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