For the expected utility model with state dependent utilities, Karni, Schmeidler and Vind (1983) have shown how to recover uniquely the involved subjective probabilities if the preferences, contingent on a hypothetical probability distribution over the state space, are known. This they do for consequence spaces, consisting of lotteries on sets of prizes. We adapt their work to consequence spaces that are connected topological spaces, without using lotteries on them. E.g. our consequences may be money, or commodity bundles.

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Mathematical Social Sciences
Erasmus School of Economics

Wakker, P. (1987). Subjective Probabilities for State-Dependent Continuous Utility. Mathematical Social Sciences, 14(3), 289–298. doi:10.1016/0165-4896(87)90007-2