We analyze three rules for updating neo-additive capacities. Only for Generalized Bayesian Updating is relative optimism the same for both updated and unconditional capacities. For updates of the other two, either the updated capacity is fully optimistic or fully pessimistic.

Kicking off the discussion following Savage's presentation at the 1952 Paris colloquium, Arrow raised what he considered to be a difficulty with the intuitive interpretation of Savage's theorem. It suggests that decision makers strictly prefer betting on an event of measure zero over betting on...

This paper exposes a difficulty in applying the revealed preference methodology to the definition of subjective probabilities. It shows that in the presence of unknowable states it is impossible to provide choice-based foundations of prior probabilities in Bayes' theory.