Lexicographic Refinements in the Context of Possibilistic Decision Theory

In Possibilistic Decision Theory (PDT), decisions are ranked by a pessimistic and an optimistic qualitative criteria. The preference relations induced by these criteria have been axiomatized by corresponding sets of rationality postulates, both à la Neumann-Morgenstern and à la Savage. In this paper we first address a particular issue regarding the axiomatic systems of PDT à la von Neumann and Morgenstern. Namely, we show how to adapt the axiomatic systems for the pessimistic and optimistic criteria when finiteness assumptions in the original model are dropped. Second, we show that a recent axiomatic approach by Giang and Shenoy using binary utilities can be captured by preference relations defined as lexicographic refinements of the above two criteria. We also provide an axiomatic characterization of these lexicographic refinements.