Inproceedings,
Interpreting, Axiomatising and Representing Coherent Choice Functions in Terms of Desirability
Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, volume 103 of Proceedings of Machine Learning Research, page 125--134. Thagaste, Ghent, Belgium, PMLR, (03--06 Jul 2019)
Abstract
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 appear in imprecise-probabilistic decision making. We provide these choice functions with a clear interpretation in terms of desirability, use this interpretation to derive a set of basic coherence axioms, and show that this notion of coherence leads to a representation in terms of sets of strict preference orders. By imposing additional properties such as totality, the mixing property and Archimedeanity, we obtain representation in terms of sets of strict total orders, lexicographic probability systems, coherent lower previsions or linear previsions.
