The Distorted Theory of Rank-Dependent Expected Utility

This paper re-examines the rank-dependent expected utility theory. Firstly, we follow Quiggin's assumption (Quiggin 1982) to deduce the rank-dependent expected utility formula over lotteries and hence extend it to the case of general random variables. Secondly, we utilize the distortion function which reflects decision-makers' beliefs to propose a distorted independence axiom and then to prove the representation theorem of rank-dependent expected utility. Finally, we make direct use of the distorted independence axiom to explain the Allais paradox and the common ratio effect.