The well-known principle that a decision maker's subjective probabilities are determined from his preferences among finite compound lotteries is developed in an especially transparent approach. This development can be easily modified to give versions of the result in a variety of infinite contexts.
"Induced Priors in Decision Problems." Ann. Statist. 5 (1) 182 - 184, January, 1977. https://doi.org/10.1214/aos/1176343751