A Desirability-Based Axiomatisation for Coherent Choice Functions
Artificial Intelligence
2018-06-05 v1 Probability
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 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.
Cite
@article{arxiv.1806.01044,
title = {A Desirability-Based Axiomatisation for Coherent Choice Functions},
author = {Jasper De Bock and Gert de Cooman},
journal= {arXiv preprint arXiv:1806.01044},
year = {2018}
}