When Savage's The Foundations of Statistics first appeared, it was a truly revolutionary work and for instances in which its axioms are applicable, it still today provides a natural set of axioms. There are at least two implicit limitations of the Savage axiomatization, however. The first is that it does not allow for a discrete state space and that it hence can not provide a solid axiomatizations for such models. The second is that it implicitly requires state independent preferences. There are many interestings applications which utilize finite state spaces and/or state dependent preferences.
In order to allow for state dependent preferences, I follow an approach similar to Karni (2003), which utilizes introspective preference relations on lotteries in additions to preference relations on acts linked together through consistency axioms. My approach differs from his in two regards. The first (and most critical) difference is that while Karni defines his introspective preference relation on the space of lotteries over all states and acts L(S*A), I define it over the the product space between lotteries over states with acts L(S)*A. The second difference between my approach and that of Karni is that I allow for a finite state space.
The first paper below provides for an extension of the von Neumann and Morgenstern expected utility representation in the framework of an introspective preference relation. The second provides the axiomatization for subjective probability, while the third utilizes state-dependent preferences in a model for an economy with differential information. All of these are still papers are still work in progress and should not be quoted.
Nygren, K. A More Complete Extension of a Theorem of von Neumann and Morgenstern. Unpublished Manuscript. 2002.
Nygren, K. An Axiomatization for State-Dependent Preferences and Subjective Probability. Unpublished Manuscript. 2002.
Nygren, K. The Existence and Strong Informational Efficiency of Perfect State-w Compeitive Equilibria in a State Contingent Claims Model with Differential Information. Unpublished Manuscript. 2002.