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

Abstract

In this paper we analyze two recent axiomatic approaches proposed by Dubois et al., and by Giang and Shenoy, respectively, for qualitative decision making where uncertainty is described by possibility theory. Both axiomtizations are inspired by von Neumann and Morgenstern's system of axioms for the case of probability theory. We show that our approach naturally unifies two axiomatic systems that correspond, respectively, to pessimistic and optimistic decision criteria proposed 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 imposes order on set of standard lotteries, and (ii) using a binary utility scale in which each utility level is represented by a pair of numbers.