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Dynamics of Inductive Inference in a Unified Framework

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  • Itzhak Gilboa

    (Tel-Aviv University; HEC, Paris; Cowles Foundation, Yale University)

  • Larry Samuelson

    ()
    (Cowles Foundation, Yale University)

  • David Schmeidler

    (Ohio State University; Tel-Aviv University)

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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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1811.

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Length: 43 pages
Date of creation: Jul 2011
Date of revision:
Publication status: Published in Journal of Economic Theory (July 2013), 148(4): 1399-1432
Handle: RePEc:cwl:cwldpp:1811

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Related research

Keywords: Induction; Bayesian updating; Case-Based Reasoning; Inference;

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References

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  1. Gilboa, I. & Schmeidler, D., 1999. "Inductive Inference: an Axiomatic Approach," Papers 29-99, Tel Aviv.
  2. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345, April.
  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 & Larry Samuelson, 2009. "Subjectivity in Inductive Inference," Levine's Working Paper Archive 814577000000000324, David K. Levine.
  5. Matsui, Akihiko, 2000. "Expected utility and case-based reasoning," Mathematical Social Sciences, Elsevier, vol. 39(1), pages 1-12, January.
  6. Hume, David, 1758. "An Equiry Concerning Human Understanding," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number hume1758.
  7. Itzhak Gilboa & David Schmeidler, 1991. "Updating Ambiguous Beliefs," Discussion Papers 924, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  9. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521517324, April.
  10. Itzhak Gilboa & David Schmeidler, 1992. "Case-Based Decision Theory," Discussion Papers 994, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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