Extending choice assessments to choice functions: An algorithm for computing the natural extension

This leads to a single optimal decision, or a set of optimal decisions all of which are equivalent. In the theory of imprecise probabilities, where multiple probabilistic models are considered simultaneously, this decision rule can be generalised in multiple ways; Troffaes [1] provides a nice overview. A typical feature of the resulting decision rules is that they will not always yield a single optimal decision, as a decision that is optimal in one probability model may for example be suboptimal in another. We here take this generalisation yet another step further by adopting the theory of choice functions: a mathematical framework for decision-making that incorporates several (imprecise) decision rules as special cases, including the classical approach of maximising expected utility [2, 3, 4]. An important feature of this framework of choice functions is that it allows one to impose axioms directly on the decisions that are represented by such a choice function [3, 4, 5].