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

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  • Herzberg, Frederik

    (Center for Mathematical Economics, Bielefeld University)

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.

Suggested Citation

  • Herzberg, Frederik, 2015. "Social choice of convex risk measures through Arrovian aggregation of variational preferences," Center for Mathematical Economics Working Papers 432, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:432
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    File URL: https://pub.uni-bielefeld.de/download/2788391/2788392
    File Function: First Version, 2010
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    Keywords

    convex risk measure; multiple priorspreferences; variational preferences; abstract aggregation theory; judgment aggregation; Arrow-type preference aggregation; model theory; first-order predicate logic; ultraproduct; ultrafilter;

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