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

In this paper we analyze two recent axiomatic approaches proposed by Dubois et al. [5] and by Giang and Shenoy [10] for qualita­ tive decision making where uncertainty is de­ scribed by possibility theory. Both axiom­ tizations are inspired by von Neumann and Morgenstern's system of axioms for the case of probability theory. We show that our ap­ proach naturally unifies two axiomatic sys­ tems that correspond, respectively, to pes­ simistic and optimistic decision criteria pro­ posed by Dubois et al. The simplifying uni­ fication is achieved by (i) replacing axioms that are supposed to reflect two informational attitudes (uncertainty aversion and uncer­ tainty attraction) by an axiom that imposes order on set of standard lotteries, and ( ii) us­ ing a binary utility scale in which each utility level is represented by a pair of numbers.