IDEAS home Printed from https://ideas.repec.org/a/spr/minsoc/v2y2001i1p77-98.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Guido Fioretti, 2001. "A mathematical theory of evidence for G.L.S. Shackle," Mind & Society: Cognitive Studies in Economics and Social Sciences, Springer;Fondazione Rosselli, vol. 2(1), pages 77-98, March.
    • Handle: RePEc:spr:minsoc:v:2:y:2001:i:1:p:77-98
    DOI: 10.1007/BF02512076
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/BF02512076
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/BF02512076?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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. Sarin, Rakesh K & Wakker, Peter, 1992. "A Simple Axiomatization of Nonadditive Expected Utility," Econometrica, Econometric Society, vol. 60(6), pages 1255-1272, November.
    4. 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.
    5. 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..
    6. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    7. J. L. Ford, 1987. "Economic Choice Under Uncertainty," Books, Edward Elgar Publishing, number 170.
    8. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alexander Zimper, 2011. "Do Bayesians Learn Their Way Out of Ambiguity?," Decision Analysis, INFORMS, vol. 8(4), pages 269-285, December.
    2. Philippe, Fabrice, 2000. "Cumulative prospect theory and imprecise risk," Mathematical Social Sciences, Elsevier, vol. 40(3), pages 237-263, November.
    3. Guido Fioretti, 2004. "Evidence Theory: A Mathematical Framework For Unpredictable Hypotheses," Metroeconomica, Wiley Blackwell, vol. 55(4), pages 345-366, November.
    4. Zimper, Alexander, 2009. "Half empty, half full and why we can agree to disagree forever," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 283-299, August.
    5. Ludwig, Alexander & Zimper, Alexander, 2006. "Investment behavior under ambiguity: The case of pessimistic decision makers," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 111-130, September.
    6. Zimper, Alexander, 2012. "Asset pricing in a Lucas fruit-tree economy with the best and worst in mind," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 610-628.
    7. Olivier L’Haridon & Lætitia Placido, 2010. "Betting on Machina’s reflection example: an experiment on ambiguity," Theory and Decision, Springer, vol. 69(3), pages 375-393, September.
    8. Aurélien Baillon & Han Bleichrodt & Umut Keskin & Olivier l’Haridon & Chen Li, 2018. "The Effect of Learning on Ambiguity Attitudes," Management Science, INFORMS, vol. 64(5), pages 2181-2198, May.
    9. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2024. "Who saves more, the naive or the sophisticated agent?," Journal of Economic Theory, Elsevier, vol. 219(C).
    10. Veronika Köbberling & Peter P. Wakker, 2003. "Preference Foundations for Nonexpected Utility: A Generalized and Simplified Technique," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 395-423, August.
    11. Izhakian, Yehuda, 2017. "Expected utility with uncertain probabilities theory," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 91-103.
    12. Alexander Zimper, 2008. "Asset pricing in a Lucas ‘fruit-tree’ economy with non-additive beliefs," Working Papers 092, Economic Research Southern Africa.
    13. Alexander Zimper, 2012. "The emergence of “fifty-fifty” probability judgements in a conditional Savage world," Working Papers 291, Economic Research Southern Africa.
    14. repec:awi:wpaper:0448 is not listed on IDEAS
    15. Jürgen Eichberger & Simon Grant & David Kelsey, 2012. "When is ambiguity–attitude constant?," Journal of Risk and Uncertainty, Springer, vol. 45(3), pages 239-263, December.
    16. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2016. "A life-cycle model with ambiguous survival beliefs," Journal of Economic Theory, Elsevier, vol. 162(C), pages 137-180.
    17. Junyi Chai & Zhiquan Weng & Wenbin Liu, 2021. "Behavioral Decision Making in Normative and Descriptive Views: A Critical Review of Literature," JRFM, MDPI, vol. 14(10), pages 1-14, October.
    18. Alexander Zimper, 2011. "Re-examining the law of iterated expectations for Choquet decision makers," Theory and Decision, Springer, vol. 71(4), pages 669-677, October.
    19. Mohammed Abdellaoui & Horst Zank, 2023. "Source and rank-dependent utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 949-981, May.
    20. Yehuda Izhakian, 2012. "Ambiguity Measurement," Working Papers 12-01, New York University, Leonard N. Stern School of Business, Department of Economics.
    21. De Waegenaere, A.M.B. & Wakker, P.P., 1997. "Choquet Integrals With Respect to Non-Monotonic Set Functions," Other publications TiSEM 85f2b7aa-da15-4c19-9765-b, Tilburg University, School of Economics and Management.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:minsoc:v:2:y:2001:i:1:p:77-98. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.