Utility-uncertainty trade-off structures

A qualitative axiomatization of a generalization of expected utility theory is given in which the expected value of simple gambles is not necessarily the product of subjective probability and utility. Representation and uniqueness theorems for these generalized structures are derived for both Archimedean and nonarchimedean cases. It is also shown that a simple condition called distributivity is necessary and sufficient in the case of simple gambles for one of these generalized expected utility structures to have simultaneously an additive subjective probability function and a multiplicative combining rule for expected values.