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In this paper we analyze two recent axiomatic approaches proposed by Duboiset al and by Giang and Shenoy to qualitative decision making where uncertaintyis described by possibility theory. Both axiomtizations are inspired by vonNeumann and Morgenstern's system of axioms for the case of probability theory.We show that our approach naturally unifies two axiomatic systems thatcorrespond respectively to pessimistic and optimistic decision criteriaproposed by Dubois et al. The simplifying unification is achieved by (i)replacing axioms that are supposed to reflect two informational attitudes(uncertainty aversion and uncertainty attraction) by an axiom that imposesorder on set of standard lotteries and (ii) using a binary utility scale inwhich each utility level is represented by a pair of numbers.

A Comparison of Axiomatic Approaches to Qualitative Decision Making Using Possibility Theory