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Dynamics of inductive inference in a unified framework

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  • Gilboa, Itzhak
  • Samuelson, Larry
  • Schmeidler, David

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 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

  • Gilboa, Itzhak & Samuelson, Larry & Schmeidler, David, 2013. "Dynamics of inductive inference in a unified framework," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1399-1432.
  • Handle: RePEc:eee:jetheo:v:148:y:2013:i:4:p:1399-1432
    DOI: 10.1016/j.jet.2012.11.004
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    References listed on IDEAS

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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. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    3. 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.
    4. Itzhak Gilboa & David Schmeidler, 1995. "Case-Based Decision Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 110(3), pages 605-639.
    5. Samuelson, Larry & Gilboa, Itzhak, 2012. "Subjectivity in inductive inference," Theoretical Economics, Econometric Society, vol. 7(2), May.
    6. Massimo Marinacci, 1996. "Decomposition and Representation of Coalitional Games," Mathematics of Operations Research, INFORMS, vol. 21(4), pages 1000-1015, November.
    7. Itzhak Gilboa & David Schmeidler, 1995. "Canonical Representation of Set Functions," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 197-212, February.
    8. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    9. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521741231.
    10. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345.
    11. Matsui, Akihiko, 2000. "Expected utility and case-based reasoning," Mathematical Social Sciences, Elsevier, vol. 39(1), pages 1-12, January.
    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.
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    Cited by:

    1. 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.
    2. Chollete, Loran & Schmeidler, David, 2014. "Demand-Theoretic Approach to Choice of Priors," UiS Working Papers in Economics and Finance 2014/14, University of Stavanger.

    More about this item

    Keywords

    Induction; Learning; Analogies; Theories; Case-based reasoning; Rule-based reasoning;

    JEL classification:

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

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