Imprecise Decision-Making: From Choice Functions to Trustworthy Machine Learning

In the realm of decision-making under uncertainty, traditional models often rely on precise probabilities and utilities to guide choices, ordering options based on their expected utility. This approach is not only easily applicable, but also backed up by a clean axiomatic characterization. The assumptions it requires are however often unrealistic. This talk considers the more general setting of imprecise decision-making, where uncertainty is no longer represented by a single probability distribution, but by more expressive uncertainty models such as sets of probability distributions or preference orders. I intend to cover a broad range of aspects of this more general type of decision making, starting from its axiomatic characterization using choice functions all the way up to its recent use in machine learning to assess the trustworthiness of automated predictions. Mathematical details are deliberately kept to a minimum, focussing instead on the main ideas and their philosophical implications.