Parametric weighting functions

This paper provides preference foundations for parametric weighting functions under rank-dependent utility. This is achieved by decomposing the independence axiom of expected utility into separate meaningful properties. These conditions allow us to characterize rank-dependent utility with power and exponential weighting functions. Moreover, by allowing probabilistic risk attitudes to vary within the probability interval, a preference foundation for rank-dependent utility with parametric inverse-S shaped weighting function is obtained.