Social choice of convex risk measures through Arrovian aggregation of variational preferences
| Autor: | Herzberg, Frederik |
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| Rok vydání: | 2015 |
| Předmět: |
abstract aggregation theory
Arrow-type preference aggregation convex risk measure first-order predicate logic Soziale Wohlfahrtsfunktion variational preferences Unmöglichkeitstheorem judgment aggregation Präferenztheorie D71 Aggregation ultraproduct model theory convex risk measure multiple priorspreferences variational preferences abstract aggregation theory judgment aggregation Arrow-type preference aggregation model theory first-order predicate logic ultraproduct ultrafilter ddc:330 multiple priorspreferences multiple priors preferences G11 Nutzenfunktion Risikomaß ultrafilter Theorie |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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