Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/43803
Authors: 
Herzberg, Frederik
Year of Publication: 
2010
Series/Report no.: 
Working papers // Institute of Mathematical Economics 432
Abstract: 
This paper studies collective decision making with regard to convex risk measures: It addresses the question whether there exist nondictatorial aggregation functions of convex risk measures satisfying Arrow-type rationality axioms (weak universality, systematicity, Pareto principle). Herein, convex risk measures are identified with variational preferences on account of the Maccheroni-Marinacci-Rustichini (2006) axiomatisation of variational preference relations and the Föllmer-Schied (2002, 2004) representation theorem for concave monetary utility functionals. We prove a variational analogue of Arrow's impossibility theorem for finite electorates. For infinite electorates, the possibility of rational aggregation depends on a uniform continuity condition for the variational preference profiles; we prove variational analogues of both Campbell's impossibility theorem and Fishburn's possibility theorem. The proof methodology is based on a model-theoretic approach to aggregation theory inspired by Lauwers-Van Liedekerke (1995). An appendix applies the Dietrich-List (2010) analysis of majority voting to the problem of variational preference aggregation.
Subjects: 
Arrow-type preference aggregation
judgment aggregation
abstract aggregation theory
variational preferences
multiple priors preferences
convex risk measure
model theory
first-order predicate logic
ultrafilter
ultraproduct
JEL: 
D71
G11
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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