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

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Working Papers ; No. 432

Classification and Topics

• Classification: Wirtschaft ; Social Choice; Clubs; Committees; Associations ; Portfolio Choice; Investment Decisions
• Subject: 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 ; Nutzenfunktion ; Präferenztheorie ; Aggregation ; Soziale Wohlfahrtsfunktion ; Risikomaß ; Unmöglichkeitstheorem ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Herzberg, Frederik
• Event: Veröffentlichung
• (who): Bielefeld University, Institute of Mathematical Economics (IMW)
• (where): Bielefeld
• (when): 2010

Further information

• Handle: http://hdl.handle.net/10419/43803
• URN: urn:nbn:de:hbz:361-17044
• Last update: 10.03.2025, 11:44 AM CET