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 and by Giang and Shenoy to 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.
