Desirability foundations of robust rational decision making

Recent work has formally linked the traditional axiomatisation of incomplete preferences a la Anscombe-Aumann with the theory of desirability developed in the context of imprecise probability, by showing in particular that they are the very same theory. The equivalence has been established under the constraint that the set of possible prizes is finite. In this paper, we relax such a constraint, thus de facto creating one of the most general theories of rationality and decision making available today. We provide the theory with a sound interpretation and with basic notions, and results, for the separation of beliefs and values, and for the case of complete preferences. Moreover, we discuss the role of conglomerability for the presented theory, arguing that it should be a rationality requirement under very broad conditions.

Automated summary

Recent work has formally linked the axiomatisation of incomplete preferences with the theory of desirability in the context of imprecise probability, showing that they are essentially the same theory. The equivalence has been established under the constraint of a finite set of possible prizes. This paper relaxes this constraint, creating one of the most general theories of rationality and decision making, and discusses the role of conglomerability as a rationality requirement.