Aggregation of Monotonic Bernoullian Archimedean Preferences: Arrovian Impossibility Results

16 Pages Posted: 20 Oct 2013

See all articles by Frederik Herzberg

Frederik Herzberg

Bielefeld University - Center for Mathematical Economics

Date Written: September 20, 2013

Abstract

Cerreia-Vioglio, Ghirardato, Maccheroni, Marinacci and Siniscalchi (Economic Theory, 48:341--375, 2011) have recently proposed a very general axiomatisation of preferences in the presence of ambiguity, viz. Monotonic Bernoullian Archimedean (MBA) preference orderings. This paper investigates the problem of Arrovian aggregation of such preferences -- and proves dictatorial impossibility results for both finite and infinite populations. Applications for the special case of aggregating expected-utility preferences are given. A novel proof methodology for special aggregation problems, based on model theory (in the sense of mathematical logic), is employed.

Keywords: ambiguity, Knightian uncertainty, expected utility, Monotonic Bernoullian Archimedean (MBA) preferences, Arrovian social choice, Arrow's theorem, impossibility result, ultrafilter, ultraproduct

JEL Classification: D71, D81, C02

Suggested Citation

Herzberg, Frederik, Aggregation of Monotonic Bernoullian Archimedean Preferences: Arrovian Impossibility Results (September 20, 2013). Institute of Mathematical Economics Working Paper No. 488, Available at SSRN: https://ssrn.com/abstract=2342431 or http://dx.doi.org/10.2139/ssrn.2342431

Frederik Herzberg (Contact Author)

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

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