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

The mental health of university students in the United Kingdom

There are increasing concerns globally about the mental health of students (Kadison,& Digeronimo, 2004). In the UK, the actual incidence of mental disturbance is unknown, although university counselling services report increased referrals (Association of University & College Counselling, 2011). This study assesses the levels of mental illness in undergraduate students to examine whether widening participation in education has resulted in increases as hypothesized by the UK Royal College of Psychiatrists (2003, 2011). Patterns of disturbance across years are compared to identify where problems arise. Students (N = 1197) completed the General Health Questionnaire-28 either on day one at university or midway through the academic year for first, second and third year students. Rates of mental illness in students equalled those of the general population but only 5.1% were currently receiving treatment. Second year students reported the most significant increases in psychiatric symptoms. Factors contributing to the problem are discussed

Independence Properties Vis-À-Vis Several Utility Representations

A detailed theoretical analysis is presented of what five utility representations – subjective expected utility (SEU), rank-dependent (cumulative or Choquet) utility (RDU), gains decomposition utility (GDU), rank weighted utility (RWU), and a configural-weight model (TAX) that we show to be equivalent to RWU – say about a series of independence properties, many of which were suggested by M. H. Birnbaum and his coauthors. The goal is to clarify what implications to draw about the descriptive aspects of the representations from data concerning these properties. The upshot is a sharp rejection of SEU and RDU and no clear choice between GDU and TAX, but a list of 8 properties is given that should receive more attention to discriminate between the latter two models. Copyright Springer 2005Independence properties, Rank-dependent utility, Rank weighted utility, TAX utility, Weighted utility,