A longer version of this paper is available from KU Scholarworks as Giang, P. H. and P. P. Shenoy, "Two Axiomatic Approaches to Decision Making Using Possibility Theory," European Journal of Operational Research, Vol. 162, No. 2, 2005, pp. 450--467.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.The research was supported by a grant from the School of Business PhD Summer Research Fund to both authors.