This paper investigates a purely qualitative approach to decision making under uncertainty. Since the pioneering work of Savage, most models of decision under uncertainty rely on a numerical representation where utility and uncertainty are commensurate. Giving up this tradition, we relax this assumption and introduce an axiom of ordinal invariance requiring that the Decision Maker's preference between two acts only depends on the relative position of their consequences for each state. Within this qualitative framework, we determine the only possible form of the corresponding decision rule. Then assuming the transitivity of the strict preference, the underlying partial confidence relations are those at work in non-monotonic inference and thus satisfy one of the main properties of possibility theory. The satisfaction of additional postulates of unanimity and anonymity enforces the use of a necessity measure, unique up to a monotonic transformation, for encoding the relative likelihood of events.
['Didier Dubois', 'Hélène Fargier', 'Patrice Perny']
Qualitative decision theory with preference relations and comparative uncertainty: an axiomatic approach