A Comparison of Axiomatic Approaches to Qualitative Decision Making Using Possibility Theory
This work provides a theoretical unification for researchers in decision theory, but it is incremental as it builds on existing axiomatic systems without introducing a new paradigm.
The paper tackles the problem of unifying two axiomatic approaches to qualitative decision making under uncertainty described by possibility theory, showing that their approach naturally unifies pessimistic and optimistic decision criteria by replacing certain axioms and using a binary utility scale.
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.