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Dynamics of Inductive Inference in a Unified Framework

Author

Listed:
  • Itzhak Gilboa

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique, TAU - Tel Aviv University, Cowles Foundation for Research in Economics - Yale University [New Haven])

  • Larry Samuelson

    (Department of Economics - Yale University [New Haven])

  • David Schmeidler

    (Department of Cell and Developmental Biology - TAU - Tel Aviv University - Sackler Faculty of Medicine, OSU - The Ohio State University [Columbus])

Abstract
We present a model of inductive inference that includes, as special cases, Bayesian reasoning, case-based reasoning, and rulebased reasoning. This uni ed framework allows us to examine how the various modes of inductive inference can be combined and how their relative weights change endogenously. For example, we establish conditions under which an agent who does not know the structure of the data generating process will decrease, over the course of her reasoning, the weight of credence put on Bayesian vs. non-Bayesian reasoning. We illustrate circumstances under which probabilistic models are used until an unexpected outcome occurs, whereupon the agent resorts to more basic reasoning techniques, such as case-based and rule-based reasoning, until enough data are gathered to formulate a new probabilistic model.

Suggested Citation

  • Itzhak Gilboa & Larry Samuelson & David Schmeidler, 2012. "Dynamics of Inductive Inference in a Unified Framework," Working Papers hal-00712823, HAL.
    • Handle: RePEc:hal:wpaper:hal-00712823
    Note: View the original document on HAL open archive server: https://hec.hal.science/hal-00712823
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    References listed on IDEAS

    as
    1. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    2. Ron Alquist & Lutz Kilian, 2010. "What do we learn from the price of crude oil futures?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 539-573.
    3. Itzhak Gilboa & David Schmeidler, 1995. "Case-Based Decision Theory," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(3), pages 605-639.
    4. , & ,, 2012. "Subjectivity in inductive inference," Theoretical Economics, Econometric Society, vol. 7(2), May.
    5. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    6. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345.
    7. Matsui, Akihiko, 2000. "Expected utility and case-based reasoning," Mathematical Social Sciences, Elsevier, vol. 39(1), pages 1-12, January.
    8. Massimo Marinacci, 1996. "Decomposition and Representation of Coalitional Games," Mathematics of Operations Research, INFORMS, vol. 21(4), pages 1000-1015, November.
    9. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521517324, September.
    10. Itzhak Gilboa & David Schmeidler, 1992. "Canonical Representation of Set Functions," Discussion Papers 986, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    12. Hume, David, 1758. "An Equiry Concerning Human Understanding," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number hume1758.
    13. Itzhak Gilboa & David Schmeidler, 1995. "Canonical Representation of Set Functions," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 197-212, February.
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    Citations

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    Cited by:

    1. Chollete, Loran & Schmeidler, David, 2014. "Demand-Theoretic Approach to Choice of Priors," UiS Working Papers in Economics and Finance 2014/14, University of Stavanger.
    2. Larbi Alaoui & Antonio Penta, 2018. "Cost-benefit analysis in reasoning," Economics Working Papers 1621, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Gilboa, Itzhak & Samuelson, Larry & Schmeidler, David, 2022. "Learning (to disagree?) in large worlds," Journal of Economic Theory, Elsevier, vol. 199(C).
    4. Annie Liang, 2016. "Games of Incomplete Information Played by Statisticians," PIER Working Paper Archive 16-028, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Jan 2016.
    5. Gilboa, Itzhak & Minardi, Stefania & Samuelson, Larry, 2020. "Theories and cases in decisions under uncertainty," Games and Economic Behavior, Elsevier, vol. 123(C), pages 22-40.
    6. John Rust, 2014. "The Limits of Inference with Theory: A Review of Wolpin (2013)," Journal of Economic Literature, American Economic Association, vol. 52(3), pages 820-850, September.
    7. Marsay, David, 2016. "Decision-making under radical uncertainty: An interpretation of Keynes' treatise," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 10, pages 1-31.

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    More about this item

    Keywords

    dynamics; inductive inference; uni ed framework;
    All these keywords.

    JEL classification:

    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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