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

Herzberg F (2010) Working Papers. Institute of Mathematical Economics; 432.
Bielefeld: Center for Mathematical Economics.

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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.
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Herzberg F. Social choice of convex risk measures through Arrovian aggregation of variational preferences. Working Papers. Institute of Mathematical Economics. Vol 432. Bielefeld: Center for Mathematical Economics; 2010.
Herzberg, F. (2010). Social choice of convex risk measures through Arrovian aggregation of variational preferences (Working Papers. Institute of Mathematical Economics, 432). Bielefeld: Center for Mathematical Economics.
Herzberg, F. (2010). Social choice of convex risk measures through Arrovian aggregation of variational preferences. Working Papers. Institute of Mathematical Economics, 432, Bielefeld: Center for Mathematical Economics.
Herzberg, F., 2010. Social choice of convex risk measures through Arrovian aggregation of variational preferences, Working Papers. Institute of Mathematical Economics, no.432, Bielefeld: Center for Mathematical Economics.
F. Herzberg, Social choice of convex risk measures through Arrovian aggregation of variational preferences, Working Papers. Institute of Mathematical Economics, vol. 432, Bielefeld: Center for Mathematical Economics, 2010.
Herzberg, F.: Social choice of convex risk measures through Arrovian aggregation of variational preferences. Working Papers. Institute of Mathematical Economics, 432. Center for Mathematical Economics, Bielefeld (2010).
Herzberg, Frederik. Social choice of convex risk measures through Arrovian aggregation of variational preferences. Bielefeld: Center for Mathematical Economics, 2010. Working Papers. Institute of Mathematical Economics. 432.
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