This paper provides simpler and more general preference foundations for difference representations than known before and shows how to obtain cardinal utility from those difference representations. In addition, this paper unifies all earlier derivations of cardinal utility by showing that they...

Proper scoring rules provide convenient and highly efficient tools for incentive-compatible elicitations of subjective beliefs. As traditionally used, however, they are valid only under expected value maximization. This paper shows how they can be generalized to modern ("non-expected utility")...