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Dynamics of Inductive Inference in a Unified Framework

  • Itzhak Gilboa
  • Larry Samuelson
  • David Schmeidler

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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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 786969000000000156.

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Date of creation: 31 Jul 2011
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Handle: RePEc:cla:levarc:786969000000000156
Contact details of provider: Web page: http://www.dklevine.com/

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  1. Itzhak Gilboa & Larry Samuelson, 2012. "Subjectivity in Inductive Inference," Working Papers hal-00756342, HAL.
  2. Gilboa, I. & Schmeidler, D., 1999. "Inductive Inference: an Axiomatic Approach," Papers 29-99, Tel Aviv.
  3. Itzhak Gilboa & David Schmeidler, 1992. "Case-Based Decision Theory," Discussion Papers 994, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Itzhak Gilboa & David Schmeidler, 1995. "Canonical Representation of Set Functions," Post-Print hal-00481346, HAL.
  5. Itzhak Gilboa & David Schmeidler, 1991. "Updating Ambiguous Beliefs," Discussion Papers 924, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  7. Itzhak Gilboa & David Schmeidler, 2001. "A Theory of Case-Based Decisions," Post-Print hal-00756321, HAL.
  8. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521517324, 1.
  9. Matsui, Akihiko, 2000. "Expected utility and case-based reasoning," Mathematical Social Sciences, Elsevier, vol. 39(1), pages 1-12, January.
  10. Hume, David, 1758. "An Equiry Concerning Human Understanding," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number hume1758.
  11. Alquist, Ron & Kilian, Lutz, 2007. "What Do We Learn from the Price of Crude Oil Futures?," CEPR Discussion Papers 6548, C.E.P.R. Discussion Papers.
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