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arXiv · 1806.01044

A Desirability-Based Axiomatisation for Coherent Choice Functions

Jasper De Bock·Gert de Cooman
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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.

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Jasper De Bock, Gert de Cooman. 2018-06-04. A Desirability-Based Axiomatisation for Coherent Choice Functions. https://arxiv.org/abs/1806.01044

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