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An additively separable representation in the Savage framework

  • Hill, Brian

This paper proposes necessary and sufficient conditions for an additively separable representation of preferences in the Savage framework (where the objects of choice are acts: measurable functions from an infinite set of states to a potentially finite set of consequences). A preference relation over acts is represented by the integral over the subset of the product of the state space and the consequence space which corresponds to the act, where this integral is calculated with respect to an evaluation measure on this space. The result requires neither Savage's P3 (monotonicity) nor his P4 (weak comparative probability). Nevertheless, the representation it provides is as useful as Savage's for many economic applications.

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 145 (2010)
Issue (Month): 5 (September)
Pages: 2044-2054

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Handle: RePEc:eee:jetheo:v:145:y:2010:i:5:p:2044-2054
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Karni, Edi, 1996. "Probabilities and Beliefs," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 249-62, November.
  2. Erio Castagnoli & Marco LiCalzi, 2005. "Benchmarking real-valued acts," Microeconomics 0502001, EconWPA.
  3. Karni, E. & Mongin, P., 1997. "On the Determination of Subjective Probability by Choices," Papers 9737, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
  4. Karni, Edi & Schmeidler, David, 1993. "On the Uniqueness of Subjective Probabilities," Economic Theory, Springer, vol. 3(2), pages 267-77, April.
  5. Karni Edi, 1993. "Subjective Expected Utility Theory with State-Dependent Preferences," Journal of Economic Theory, Elsevier, vol. 60(2), pages 428-438, August.
  6. Brian, HILL, 2007. "When is there state independence?," Les Cahiers de Recherche 883, HEC Paris.
  7. Mohammed Abdellaoui & Peter Wakker, 2005. "The Likelihood Method for Decision under Uncertainty," Theory and Decision, Springer, vol. 58(1), pages 3-76, 02.
  8. Karni, Edi & Schmeidler, David & Vind, Karl, 1983. "On State Dependent Preferences and Subjective Probabilities," Econometrica, Econometric Society, vol. 51(4), pages 1021-31, July.
  9. Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
  10. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
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