Social choice of convex risk measures through Arrovian aggregation of variational preferences
AbstractIt 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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Bibliographic InfoPaper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 432.
Length: 16 pages
Date of creation: May 2010
Date of revision:
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;
Find related papers by JEL classification:
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-06-04 (All new papers)
- NEP-CDM-2010-06-04 (Collective Decision-Making)
- NEP-UPT-2010-06-04 (Utility Models & Prospect Theory)
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