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Subjectively Expected State-Independent Utility on State-Dependent Consequence Domains

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  • Peter J. Hammond

Abstract

August 1997 The standard decision theories of Savage and of Anscombe and Aumann both postulate that the domain of consequences is state independent. But this hypothesis makes no sense when, for instance, there is a risk of death or serious injury. The paper considers one possible way of deriving subjective probabilities and utilities in this case also. Moreover, the utilities will be state independent in the sense of giving equal value to any consequence that happens to occur in more than one state dependent consequence domain. The key is to consider decision trees having ``hypothetical" probabilities attached to states of nature, and even to allow hypothetical choices of these probabilities.

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Paper provided by Stanford University, Department of Economics in its series Working Papers with number 97024.

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Date of creation: Aug 1997
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Handle: RePEc:wop:stanec:97024

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  1. Roger B. Myerson, 1978. "An Axiomatic Derivation of Subjective Probability," Discussion Papers 338, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Karni, Edi, 1993. "A Definition of Subjective Probabilities with State-Dependent Preferences," Econometrica, Econometric Society, vol. 61(1), pages 187-98, January.
  3. Karni, Edi & Schmeidler, David, 1991. "Utility theory with uncertainty," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 33, pages 1763-1831 Elsevier.
  4. MONGIN, Philippe, . "The paradox of the Bayesian experts and state-dependent utility theory," CORE Discussion Papers RP -1312, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Hammond, P.J. & , ., 1987. "Consequentialist foundations for expected utility," CORE Discussion Papers 1987016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Karni Edi, 1993. "Subjective Expected Utility Theory with State-Dependent Preferences," Journal of Economic Theory, Elsevier, vol. 60(2), pages 428-438, August.
  7. Karni, Edi & Schmeidler, David & Vind, Karl, 1983. "On State Dependent Preferences and Subjective Probabilities," Econometrica, Econometric Society, vol. 51(4), pages 1021-31, July.
  8. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
  9. Machina, Mark J, 1987. "Choice under Uncertainty: Problems Solved and Unsolved," Journal of Economic Perspectives, American Economic Association, vol. 1(1), pages 121-54, Summer.
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