A Desirability-Based Axiomatisation for Coherent Choice Functions
This work addresses foundational issues in decision theory under uncertainty, offering a coherent framework for imprecise-probabilistic models, but it appears incremental as it builds on existing theories of choice functions and desirable gambles.
The paper tackled the problem of modeling choice under uncertainty using choice functions by providing a clear interpretation based on attitudes towards gambling, derived from sets of desirable gambles, and resulted in a full-fledged theory including representation and conservative inference methods.
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules to imprecise-probabilistic uncertainty models. We provide them with a clear interpretation in terms of attitudes towards gambling, borrowing ideas from the theory of sets of desirable gambles, and we use this interpretation to derive a set of basic axioms. We show that these axioms lead to a full-fledged theory of coherent choice functions, which includes a representation in terms of sets of desirable gambles, and a conservative inference method.