On the consistency of risk acceptance criteria with normative theories for decision-making

In evaluation of safety in projects it is common to use risk acceptance criteria to support decision-making. In this paper, we discuss to what extent the risk acceptance criteria is in accordance with the normative theoretical framework of the expected utility theory and the rank-dependent utility theory. We show that the use of risk acceptance criteria may violate the independence axiom of the expected utility theory and the comonotonic independence axiom of the rank-dependent utility theory. Hence the use of risk acceptance criteria is not in general consistent with these theories. The level of inconsistency is highest for the expected utility theory.