Second Order Beliefs Models of Choice under Imprecise Risk: Non-additive Second Order Beliefs vs. Nonlinear Second Order Utility∗

This paper discusses models of choice under imprecise objective proba-bilistic information featuring beliefs about beliefs – second order beliefs. A new model, called Second Order Dual Expected Utility (SODEU) featuring non-additive second order beliefs is introduced, axiomatized and systemati-cally contrasted with the leading alternative model of this kind, the Second Order Subjective Expected Utility (SOSEU) model (Klibanoff, Marinacci, and Mukerji, 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