IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1811.html
   My bibliography  Save this paper

Dynamics of Inductive Inference in a Unified Framework

Author

Listed:

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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d18/d1811.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. , & ,, 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.
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Gilboa, Itzhak & Samuelson, Larry & Schmeidler, David, 2022. "Learning (to disagree?) in large worlds," Journal of Economic Theory, Elsevier, vol. 199(C).
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
    2. O’Callaghan, Patrick, 2011. "Context and Decision: Utility on a Union of Mixture Spaces," The Warwick Economics Research Paper Series (TWERPS) 973, University of Warwick, Department of Economics.
    3. Marinacci, Massimo, 1999. "Limit Laws for Non-additive Probabilities and Their Frequentist Interpretation," Journal of Economic Theory, Elsevier, vol. 84(2), pages 145-195, February.
    4. Bleile, Jörg, 2016. "Cautious Belief Formation," Center for Mathematical Economics Working Papers 507, Center for Mathematical Economics, Bielefeld University.
    5. O'Callaghan, Patrick, 2011. "Context and Decision: Utility on a Union of Mixture Spaces," Economic Research Papers 270751, University of Warwick - Department of Economics.
    6. Heyen, Daniel, 2018. "Ambiguity aversion under maximum-likelihood updating," LSE Research Online Documents on Economics 80342, London School of Economics and Political Science, LSE Library.
    7. Daron Acemoglu & Asuman Ozdaglar, 2011. "Opinion Dynamics and Learning in Social Networks," Dynamic Games and Applications, Springer, vol. 1(1), pages 3-49, March.
    8. Aouani, Zaier & Chateauneuf, Alain, 2008. "Exact capacities and star-shaped distorted probabilities," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 185-194, September.
    9. Gilboa, Itzhak & Samuelson, Larry & Schmeidler, David, 2022. "Learning (to disagree?) in large worlds," Journal of Economic Theory, Elsevier, vol. 199(C).
    10. Benjamin Radoc, 2020. "Bandit with similarity information," Department of Economics, Ateneo de Manila University, Working Paper Series 202002, Department of Economics, Ateneo de Manila University.
    11. Brit Grosskopf & Rajiv Sarin & Elizabeth Watson, 2015. "An experiment on case-based decision making," Theory and Decision, Springer, vol. 79(4), pages 639-666, December.
    12. Millner, Antony & Dietz, Simon & Heal, Geoffrey, 2010. "Ambiguity and climate policy," LSE Research Online Documents on Economics 37595, London School of Economics and Political Science, LSE Library.
    13. Alain Chateauneuf & Jean-Philippe Lefort, 2006. "Some Fubini theorems on product sigma-algebras for non-additive measures," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00130444, HAL.
    14. Agastya, Murali & Slinko, Arkadii, 2015. "Dynamic choice in a complex world," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 232-258.
    15. Bleile, Jörg, 2016. "Limited Attention in Case-Based Belief Formation," Center for Mathematical Economics Working Papers 518, Center for Mathematical Economics, Bielefeld University.
    16. Wolfgang Ossadnik & Dirk Wilmsmann & Benedikt Niemann, 2013. "Experimental evidence on case-based decision theory," Theory and Decision, Springer, vol. 75(2), pages 211-232, August.
    17. Ghirardato, Paolo & Le Breton, Michel, 2000. "Choquet Rationality," Journal of Economic Theory, Elsevier, vol. 90(2), pages 277-285, February.
    18. Ghirardato, Paolo, 1997. "On Independence for Non-Additive Measures, with a Fubini Theorem," Journal of Economic Theory, Elsevier, vol. 73(2), pages 261-291, April.
    19. Alain Chateauneuf & Jean-Philippe Lefort, 2006. "Some Fubini theorems on sigma-algebras for non additive measures," Cahiers de la Maison des Sciences Economiques b06086, Université Panthéon-Sorbonne (Paris 1).
    20. O’Callaghan, Patrick H., 2018. "Axioms for measuring utility on partial mixture sets," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 76-86.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:1811. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.