Conservative decision-making with sets of probabilities: How to infer new choices from previous ones

We study a generalized version of maximizing expected utility, called E-admissibility, to make decisions when the decision-maker's uncertainty is described by a set of probability mass functions. In particular, instead of specifying this set directly, we assume that we only have partial information about the decision-maker's preferences or choices, in the form of which options she rejects from some finite sets of options. We describe both the decision-making process and the available information using choice functions, and we provide an algorithm, based on linear programming, to compute the most conservative extension of a given choice assessment to a choice function that makes decisions based on E-admissibility. Next, we relate this E-admissible extension to the so-called coherent extension and show how the same techniques that are used to simplify the computation of this coherent extension can also be used to simplify that of the E-admissible one. In our experiments, we demonstrate that decision-making with the E-admissible extension is faster and more informative than with the coherent one, but also observe that the required computations are challenging once the parameters of the problem scale.