An explicit representation for disappointment aversion and other betweenness preferences

One of the most well known models of non-expected utility is Gul's (1991) model of disappointment aversion. This model, however, is defined implicitly, as the solution to a functional equation; its explicit utility representation is unknown, which may limit its applicability. We show that an explicit representation can be easily constructed, using solely the components of the implicit representation. We also provide a more general result: an explicit representation for preferences in the betweenness class that also satisfy negative certainty independence (Dillenberger 2010) or its counterpart. We show how our approach gives a simple way to identify the parameters of the representation behaviorally and to study the consequences of disappointment aversion in a variety of applications.