Comonotonic Independence: The Critical Test between Classical and Rank-Dependent Utility Theories

This paper compares classical expected utility with the more general rank-dependent utility models. First we show that it is the difference between the independence condition for preferences of expected utility and its comonotonic generalization in rank-dependent utility, that provides the exact demarcation between the two models. Other axiomatic differences are not essential. Next an experimental design is described that tests this difference between independence and comonotonic independence in its most basic form and is robust against violations of other assumptions that may confound the results, in particular the reduction principle, transitivity, and independence of utility from events. It is well-known that in the classical counterexamples to expected utility, comonotonic independence performs better than full-force independence. In general, however, we find that comonotonic independence does not perform better. This is contrary to our prior expectation and suggests that the rank-dependent models, in full generality, do not provide a descriptive improvement over expected utility. For the future of the rank-dependent models, submodels and phenomena must be identified for which rank-dependence does contribute descriptively.