Abstract
Several axiom systems for preference amongst gambles lead to the existence of a unique probability and a state independent utility such that gambles are ranked according to their expected utilities. These axioms have been used as a foundation for Bayesian decision theory and the subjective probability calculus. We note that the uniqueness of the probability is relative to the choice of what counts as a constant outcome. Although it is sometimes clear what should be considered constant, there are many cases in which there are several possible choices. Each choice can lead to a different “unique” probability and utility. By focusing attention on state dependent utilities, we hope to determine conditions under which a truly unique probability and utility can be determined from an agent’s expressed preferences amongst gambles.
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© 1992 Springer-Verlag New York, Inc.
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Schervish, M.J., Seidenfeld, T., Kadane, J.B. (1992). Small Worlds and State Dependent Utilities. In: Goel, P.K., Iyengar, N.S. (eds) Bayesian Analysis in Statistics and Econometrics. Lecture Notes in Statistics, vol 75. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2944-5_12
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DOI: https://doi.org/10.1007/978-1-4612-2944-5_12
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