Expected utility with purely subjective non-additive probabilities

Abstract

Acts are functions from the set of states of the world into the set of consequences. Savage proposed axioms regarding a binary relation on the set of acts which are necessary and sufficient for it to be representable by the functional ʃu(·)dP for some real-valued (utility) function u on the set of consequences and a (probability) measure P on the set of states of the world. The Ellsberg paradox leads us to reject one of Savage's main axioms - the Sure Thing Principle - and develop a more general theory, in which the probability measure need not be additive.