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A Single-Stage Approach to Anscombe and Aumann's Expected Utility

Listed author(s):
  • Rakesh Sarin
  • Peter Wakker

Anscombe and Aumann showed that if one accepts the existence of a physical randomizing device such as a roulette wheel then Savage's derivation of subjective expected utility can be considerably simplified. They, however, invoked compound gambles to define their axioms. We demonstrate that the subjective expected utility derivation can be further simplified and need not invoke compound gambles. Our simplification is obtained by closely following the steps by which probabilities and utilities are elicited.

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File URL: http://hdl.handle.net/10.2307/2971720
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Article provided by Oxford University Press in its journal The Review of Economic Studies.

Volume (Year): 64 (1997)
Issue (Month): 3 ()
Pages: 399-409

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Handle: RePEc:oup:restud:v:64:y:1997:i:3:p:399-409.
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  1. Machina Mark J. & Schmeidler David, 1995. "Bayes without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice," Journal of Economic Theory, Elsevier, vol. 67(1), pages 106-128, October.
  2. Segal, Uzi, 1990. "Two-Stage Lotteries without the Reduction Axiom," Econometrica, Econometric Society, vol. 58(2), pages 349-377, March.
  3. R. Duncan Luce & Detlof von Winterfeldt, 1994. "What Common Ground Exists for Descriptive, Prescriptive, and Normative Utility Theories?," Management Science, INFORMS, vol. 40(2), pages 263-279, February.
  4. G. L. S. Shackle, 1949. "A Non-Additive Measure of Uncertainty," Review of Economic Studies, Oxford University Press, vol. 17(1), pages 70-74.
  5. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
  6. Frederick Mosteller & Philip Nogee, 1951. "An Experimental Measurement of Utility," Journal of Political Economy, University of Chicago Press, vol. 59, pages 371-371.
  7. Eichberger, Jurgen & Kelsey, David, 1996. "Uncertainty Aversion and Dynamic Consistency," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(3), pages 625-640, August.
  8. Sarin, Rakesh K & Wakker, Peter, 1992. "A Simple Axiomatization of Nonadditive Expected Utility," Econometrica, Econometric Society, vol. 60(6), pages 1255-1272, November.
  9. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
  10. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
  11. Peter H. Farquhar, 1984. "State of the Art---Utility Assessment Methods," Management Science, INFORMS, vol. 30(11), pages 1283-1300, November.
  12. Graham Loomes & Robert Sugden, 1986. "Disappointment and Dynamic Consistency in Choice under Uncertainty," Review of Economic Studies, Oxford University Press, vol. 53(2), pages 271-282.
  13. Karni, Edi, 1993. "A Definition of Subjective Probabilities with State-Dependent Preferences," Econometrica, Econometric Society, vol. 61(1), pages 187-198, January.
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