A decision maker has to choose one of several random variables, with uncertainty known distributions. As a Bayesian she behaves as if she knew the distributions. In his paper we suggest an axiomatic derivation of these (subjective) distributions, which is much more economical than the derivations by de Finetti or Savage. They derive the whole joint distribution of all the available random variables.
Gilboa, Itzhak and Schmeidler, David, "Subjective Distributions" (2001). Cowles Foundation Discussion Papers. 1603.