F. J. Anscombe and R. J. Aumann (1963) showed that, if one accepts the existence of a physical randomizing device such as a roulette wheel, then L. J. Savage's derivation of subjective expected utility can be considerably simplified. They, however, invoked compound gambles to define their...

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")...