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

This article compares classical expected utility (EU) with the more general rank-dependent utility (RDU) models. The difference between the independence condition for preferences of EU and its comonotonic generalization in RDU provides the exact demarcation between EU and rank-dependent models. Other axiomatic differences are not essential. 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 and transitivity. It is well known that in the classical counterexamples to EU, comonotonic independence performs better than full-force independence. For our more general choice pairs, however, we find that comonotonic independence does not perform better. This is contrary to our prior expectation and suggests that rank-dependent models, in full generality, do not provide a descriptive improvement over EU. For rank-dependent models to have a future, submodels and choice situations need to be identified for which rank-dependence does contribute descriptively

Combined Nonparametric Tests for the Social Sciences

The nonparametric framework is very often considered in the social sciences because the hypothesis of normality is generally not tenable. In this context, combined testing has been very useful for comparing means/medians, variability and for the location/scale problem. The aim of the paper is to see whether combined testing is useful also for general two-sample problems that arise in the social sciences. The framework of combined testing for the general two-sample problem is presented. Some tests are developed according to it. Size and power of the combined tests are investigated in a simulation study and compared to non combined tests. It is shown that the new tests compare favorably with the former ones. In particular, the new tests can be very useful when the practitioner, as very often happens when analyzing social data, has no clear idea on parent population distributions. An example of social experiment is discussed