We provide an axiomatic characterization of a family of criteria for ranking completely and/or ambiguous decisions. A completely uncertain decision is described by the set of all its consequences (assumed to be finite). An ambiguous decision is described as a set of possible probability distributions over a set of prizes. Every criterion in the family compares sets on the basis of their conditional expected utility, for some “likelihood” function taking strictly positive values and some utility function both having the universe of alternatives as their domain.

By Nicolas Gravel, Thierry Marchant, Arunava Sen

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