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A mathematical theory of evidence for G.L.S. Shackle

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  • Guido Fioretti

Abstract

Evidence Theory is a branch of mathematics that concerns the combination of empirical evidence in an individual's mind in order to construct a coherent picture of reality. Designed to deal with unexpected empirical evidence suggesting new possibilities, evidence theory has a lot in common with Shackle's idea of decision-making as a creative act. This essay investigates this connection in detail, pointing to the usefulness of evidence theory to formalise and extend Shackle's decision theory. In order to ease a proper framing of the issues involved, evidence theory is not only compared with Shackle's ideas but also with additive and sub-additive probability theories. Furthermore, the presentation of evidence theory does not refer to the original version only, but takes account of its most recent developments, too.

Suggested Citation

  • Guido Fioretti, 2001. "A mathematical theory of evidence for G.L.S. Shackle," ICER Working Papers 03-2001, ICER - International Centre for Economic Research.
    • Handle: RePEc:icr:wpicer:03-2001
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    1. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    2. 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.
    3. Donald W. Katzner, 1986. "Potential Surprise, Potential Confirmation, and Probability," Journal of Post Keynesian Economics, Taylor & Francis Journals, vol. 9(1), pages 58-78, September.
    4. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    5. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    6. J. L. Ford, 1987. "Economic Choice Under Uncertainty," Books, Edward Elgar Publishing, number 170.
    7. Germano Resconi & George J. Klir & Eliano Pessa, 1999. "Conceptual Foundations Of Quantum Mechanics: The Role Of Evidence Theory, Quantum Sets, And Modal Logic," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 29-62.
    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. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    10. Jean-Yves Jaffray & Fabrice Philippe, 1997. "On the Existence of Subjective Upper and Lower Probabilities," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 165-185, February.
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    Cited by:

    1. Fioretti, Guido, 2009. "Either, Or. Exploration of an Emerging Decision Theory," MPRA Paper 12897, University Library of Munich, Germany.
    2. Guido Fioretti, 2004. "Evidence Theory: A Mathematical Framework For Unpredictable Hypotheses," Metroeconomica, Wiley Blackwell, vol. 55(4), pages 345-366, November.
    3. Guido Fioretti, 2009. "Evidence Theory As A Procedure For Handling Novel Events," Metroeconomica, Wiley Blackwell, vol. 60(2), pages 283-301, May.

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