Qualitative decision under uncertainty: Back to expected utility

Different qualitative models have been proposed for decision under uncertainty in Artificial Intelligence, but they generally fail to satisfy the principle of strict Pareto dominance or principle of efficiency, in contrast to the classical numerical criterion – expected utility. Among the most prominent examples of qualitative models are the qualitative possibilistic utilities and the order of magnitude expected utilities. They are both appealing but inefficient in the above sense. The question is whether it is possible to reconcile qualitative criteria and efficiency. The present paper shows that the answer is yes, and that it leads to special kinds of expected utilities. It is also shown that although numerical, these expected utilities remain qualitative: they lead to different decision procedures based on min, max and reverse operators only, generalizing the leximin and leximax orderings of vectors.