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The weight of argument and non-additive measures: a note

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Marcello Basili ()
Carlo Zappia ()

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Abstract

This note argues that a representation of the epistemic state of the individual through a non-additive measure provides a novel account of Keynes’s view of probability theory proposed in his Treatise on Probability. The paper shows, first, that Keynes’s “non-numerical probabilities” can be interpreted in terms of decisional weights and distorsions of the probability priors. Second, that the degree of non-additivity of the probability measure can account for the confidence in the assessment without any reference to a second order probability. And, third, that the criterion for decision making under uncertainty derived in the non-additive literature incorporates a measure of the degree of confidence in the probability assessment. The paper emphasises the Keynesian derivation of Ellsberg’s analysis: the parallel between Keynes and Ellsberg is deemed to be significant since Ellsberg’s insights represent the main starting point of the modern developments of decision theory under uncertainty and ambiguity.

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Paper provided by Department of Economic Policy, Finance and Development (DEPFID), University of Siena in its series Department of Economic Policy, Finance and Development (DEPFID) University of Siena with number 003.

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Date of creation: Jun 2007
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Handle: RePEc:usi:depfid:003

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Related research
Keywords: uncertainty; probabilities; Keynes.;

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Find related papers by JEL classification:
B16 - Schools of Economic Thought and Methodology - - History of Economic Thought through 1925 - - - Quantitative and Mathematical
D21 - Microeconomics - - Production and Organizations - - - Firm Behavior

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Itzhak Gilboa & David Schmeidler, 1992. "Additive Representation of Non-Additive Measures and the Choquet Integral," Discussion Papers 985, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  2. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-80, November. [Downloadable!] (restricted)
  3. Anand, Paul, 1991. "The Nature of Rational Choice and The Foundations of Statistics," Oxford Economic Papers, Oxford University Press, vol. 43(2), pages 199-216, April. [Downloadable!] (restricted)
  4. Dow, James & Werlang, Sergio Ribeiro da Costa, 1992. "Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio," Econometrica, Econometric Society, vol. 60(1), pages 197-204, January. [Downloadable!] (restricted)
  5. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December. [Downloadable!] (restricted)
  6. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January. [Downloadable!] (restricted)
  7. Kelsey, David, 1994. "Maxmin Expected Utility and Weight of Evidence," Oxford Economic Papers, Oxford University Press, vol. 46(3), pages 425-44, July. [Downloadable!] (restricted)
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  8. Eichberger, J. & Kelsey, D., 1996. "E-Capacities and the Ellsberg Paradox," Discussion Papers 96-13, Department of Economics, University of Birmingham.
  9. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October. [Downloadable!] (restricted)
  10. Kelsey, David & Quiggin, John, 1992. " Theories of Choice under Ignorance and Uncertainty," Journal of Economic Surveys, Blackwell Publishing, vol. 6(2), pages 133-53.
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  11. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April. [Downloadable!] (restricted)
  12. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
  13. Fontana, Giuseppe & Gerrard, Bill, 2004. "A Post Keynesian theory of decision making under uncertainty," Journal of Economic Psychology, Elsevier, vol. 25(5), pages 619-637, October. [Downloadable!] (restricted)
  14. Einhorn, Hillel J & Hogarth, Robin M, 1986. "Decision Making under Ambiguity," Journal of Business, University of Chicago Press, vol. 59(4), pages S225-50, October. [Downloadable!] (restricted)
  15. Lawson, Tony, 1985. "Uncertainty and Economic Analysis," Economic Journal, Royal Economic Society, vol. 95(380), pages 909-27, December. [Downloadable!] (restricted)
  16. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May. [Downloadable!] (restricted)
  17. David Dequech, 2000. "Fundamental Uncertainty and Ambiguity," Eastern Economic Journal, Eastern Economic Association, vol. 26(1), pages 41-60, Winter. [Downloadable!]
  18. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March. [Downloadable!] (restricted)
  19. Runde, Jochen, 1994. "Keynesian Uncertainty and Liquidity Preference," Cambridge Journal of Economics, Oxford University Press, vol. 18(2), pages 129-44, April.
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  1. Carlo Zappia, 2008. "Non-Bayesian decision theory ante-litteram: the case of G. L. S. Shackle," Department of Economic Policy, Finance and Development (DEPFID) University of Siena 0408, Department of Economic Policy, Finance and Development (DEPFID), University of Siena. [Downloadable!]
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