Second order beliefs models of choice under imprecise risk: Nonadditive second order beliefs versus nonlinear second order utility

Abstract

This paper discusses models of choice under imprecise objective probabilistic information featuring beliefs about beliefs, i.e., second order beliefs. A new model, called second order dual expected utility, featuring nonadditive second order beliefs, is introduced, axiomatized, and systematically contrasted with the leading alternative model of this kind, i.e., the second order subjective expected utility model (Klibanoff et al. 2005, Nau 2006, Seo 2009) for which, for the sake of comparison, we provide a new axiomatization, dispensing with the complex constructs used in extant axiomatizations. Ambiguity attitude and attitude toward information in general are discussed and characterized.

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