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Dynamics of Inductive Inference in a Unified Framework

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Abstract

We present a model of inductive inference that includes, as special cases, Bayesian reasoning, case-based reasoning, and rule-based reasoning. This unified framework allows us to examine, positively or normatively, how the various modes of inductive inference can be combined and how their relative weights change endogenously. 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 show that even random data can make certain theories seem plausible and hence increase the weight of rule-based vs. case-based reasoning, leading the agent in some cases to cycle between being rule-based and case-based. We identify conditions under which minmax regret criteria will not be effective.

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  • Itzhak Gilboa & Larry Samuelson & David Schmeidler, 2011. "Dynamics of Inductive Inference in a Unified Framework," Cowles Foundation Discussion Papers 1811, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1811
    Note: CFP 1409
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    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. , & ,, 2012. "Subjectivity in inductive inference," Theoretical Economics, Econometric Society, vol. 7(2), May.
    4. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    5. 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.
    6. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345, January.
    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.
    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. Itzhak Gilboa & David Schmeidler, 1995. "Canonical Representation of Set Functions," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 197-212, February.
    13. Hume, David, 1758. "An Equiry Concerning Human Understanding," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number hume1758.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Larbi Alaoui & Antonio Penta, 2018. "Cost-benefit analysis in reasoning," Economics Working Papers 1621, Department of Economics and Business, Universitat Pompeu Fabra.
    5. Chollete, Loran & Schmeidler, David, 2014. "Demand-Theoretic Approach to Choice of Priors," UiS Working Papers in Economics and Finance 2014/14, University of Stavanger.
    6. 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.
    7. Gilboa, Itzhak & Samuelson, Larry & Schmeidler, David, 2022. "Learning (to disagree?) in large worlds," Journal of Economic Theory, Elsevier, vol. 199(C).

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    More about this item

    Keywords

    Induction; Bayesian updating; Case-Based Reasoning; Inference;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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