Axiomatic Foundations of Generalized Qualitative Utility

The aim of this paper is to provide a unifying axiomatic justification for a class of qualitative decision models comprising among others optimistic/pessimistic qualitative utilities, binary possibilistic utility, likelihood-based utility, Spohn’s disbelief function-based utility. All those criteria that are instances of Algebraic Expected Utility have been shown to be counterparts of Expected Utility thanks to a unifying axiomatization in a von Neumann-Morgenstern setting when non probabilistic decomposable uncertainty measures are used. Those criteria are based on (⊕,⊗) operators, counterpart of (+,×) used by Expected Utility, where ⊕ is an idempotent operator and ⊗ is a triangular norm. The axiomatization is lead in the Savage setting which is a more general setting than that of von Neumann-Morgenstern as here we do not assume that the uncertainty representation of the decision-maker is known.