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Title:Social choice of convex risk measures through Arrovian aggregation of variational preferences PDF Logo
Authors:Herzberg, Frederik
Issue Date: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:urn:nbn:de:hbz:361-17044
Document Type:Working Paper
Appears in Collections:Working Papers, Center for Mathematical Economics (IMW), Bielefeld University

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