Desirability

There are many ways to model uncertainty. The most widely used type of model in the literature is a function that maps something we are uncertain about to a value that expresses what we know or believe to know about it. This chapter shows that other types of models that are conceptually and intuitively attractive can be built and used as well. The focus lies on the notion of desirability and the theory of sets of desirable gambles. After an introduction to its concepts and structure, desirability is used in the chapter as a nexus for clarifying the relationships between many of the equivalent or almost equivalent models for uncertainty appearing in the imprecise-probability literature: partial preference orders, credal sets, and lower previsions.