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| Title: | | Social choice of convex risk measures through Arrovian aggregation of variational preferences  |
| 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, Institute of Mathematical Economics, Universität Bielefeld
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