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.