| Abstract: | A key feature of the rank-dependent model for decision making under risk is that the weighting of an outcome depends on its relative rank. This theory received numerous axiomatizations, however, all these sets of axioms need to make an explicit reference to the ranking of the outcomes. This situation is unsatisfactory, as it seems to be desirable to get the ranking property of this model as a consequence of the model, rather than as an assumption. [Yaari, M.E., 1987. The dual theory of choice under risk. Econometrica 55, 95–115] offered a special version of this model (called dual theory), where the utility function is linear. This paper offers a set of axioms implying Yaari’s dual theory without making any reference to the order of the outcomes. The main axiom is called semi betweenness, which, unlike the usual case, is made on random variables rather than on distribution functions. |
