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. In [Dubois and Prade, 1995] qualitative criteria based on possibility theory have been proposed, that are appealing but inefficient in the above sense. The question is whether it is possible to reconcile possibilistic 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 two different decision procedures based on min, max and reverse operators only, generalizing the leximin and leximax orderings of vectors.

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