IDEAS home Printed from https://ideas.repec.org/p/bie/wpaper/507.html
   My bibliography  Save this paper

Cautious Belief Formation

Author

Listed:
  • Bleile, Jörg

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We provide an axiomatic approach to a belief formation process in an informational environment characterized by limited, heterogenous and differently precise information. For a list of previously observed cases an agent needs to express her belief by assigning probabilities to possible outcomes. Different numbers of observations of a particular case give rise to varying precision levels associated to the pieces of information. Different precise information affects the cautiousness and confidence with which agents form estimations. We modify the Concatenation axiom introduced in Billot, Gilboa, Samet and Schmeidler (BGSS) (Econometrica, 2005) in a way to capture the impact of precision and its related perceptional effects, while still keeping its normative appealing spirit. We obtain a representation of a belief as a weighted sum of estimates induced by past cases. The estimates are affected by cautiousness and confidence considerations depending on the precision of the underlying observed information, which generalizes BGSS. The weights are determined by frequencies of the observed cases and their similarities with the problem under consideration.

Suggested Citation

  • Bleile, Jörg, 2016. "Cautious Belief Formation," Center for Mathematical Economics Working Papers 507, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:507
    as

    Download full text from publisher

    File URL: https://pub.uni-bielefeld.de/download/2901523/2902028
    File Function: First Version, 2014
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gilboa, Itzhak & Lieberman, Offer & Schmeidler, David, 2011. "A similarity-based approach to prediction," Journal of Econometrics, Elsevier, vol. 162(1), pages 124-131, May.
    2. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    3. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2012. "Probabilities as Similarity-Weighted Frequencies," World Scientific Book Chapters, in: Case-Based Predictions An Axiomatic Approach to Prediction, Classification and Statistical Learning, chapter 7, pages 169-184, World Scientific Publishing Co. Pte. Ltd..
    4. 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.
    5. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345.
    6. Eichberger, Jürgen & Guerdjikova, Ani, 2010. "Case-based belief formation under ambiguity," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 161-177, November.
    7. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2012. "Empirical Similarity," World Scientific Book Chapters, in: Case-Based Predictions An Axiomatic Approach to Prediction, Classification and Statistical Learning, chapter 9, pages 211-243, World Scientific Publishing Co. Pte. Ltd..
    8. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521517324, September.
    9. Larry G. Epstein & Martin Schneider, 2007. "Learning Under Ambiguity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(4), pages 1275-1303.
    10. Antoine Billot & Itzhak Gilboa & David Schmeidler, 2012. "Axiomatization of an Exponential Similarity Function," World Scientific Book Chapters, in: Case-Based Predictions An Axiomatic Approach to Prediction, Classification and Statistical Learning, chapter 10, pages 245-257, World Scientific Publishing Co. Pte. Ltd..
    11. Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2012. "Rationality of belief or: why savage's axioms are neither necessary nor sufficient for rationality," Post-Print hal-00745599, HAL.
    12. David S. Ahn, 2008. "Ambiguity Without a State Space," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(1), pages 3-28.
    13. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    14. , & ,, 2006. "A model of choice from lists," Theoretical Economics, Econometric Society, vol. 1(1), pages 3-17, March.
    15. Ayala Arad & Gabrielle Gayer, 2012. "Imprecise Data Sets as a Source of Ambiguity: A Model and Experimental Evidence," Management Science, INFORMS, vol. 58(1), pages 188-202, January.
    Full references (including those not matched with items on IDEAS)

    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. Eichberger, Jürgen & Guerdjikova, Ani, 2013. "Ambiguity, data and preferences for information – A case-based approach," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1433-1462.
    2. Bleile, Jörg, 2016. "Limited Attention in Case-Based Belief Formation," Center for Mathematical Economics Working Papers 518, Center for Mathematical Economics, Bielefeld University.
    3. Eichberger, Jürgen & Guerdjikova, Ani, 2010. "Case-based belief formation under ambiguity," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 161-177, November.
    4. Gayer, Gabrielle, 2010. "Perception of probabilities in situations of risk: A case based approach," Games and Economic Behavior, Elsevier, vol. 68(1), pages 130-143, January.
    5. Gilboa, Itzhak & Lieberman, Offer & Schmeidler, David, 2011. "A similarity-based approach to prediction," Journal of Econometrics, Elsevier, vol. 162(1), pages 124-131, May.
    6. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2012. "On the Definition of Objective Probabilities by Empirical Similarity," World Scientific Book Chapters, in: Case-Based Predictions An Axiomatic Approach to Prediction, Classification and Statistical Learning, chapter 11, pages 259-280, World Scientific Publishing Co. Pte. Ltd..
    7. 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.
    8. Teitelbaum, Joshua C., 2013. "Asymmetric empirical similarity," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 346-351.
    9. Eichberger, Jürgen & Guerdjikova, Ani, 2008. "Multiple Priors as Similarity Weighted Frequencies," Papers 08-07, Sonderforschungsbreich 504.
    10. 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.
    11. Agastya, Murali & Slinko, Arkadii, 2015. "Dynamic choice in a complex world," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 232-258.
    12. Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2007. "Probabilities in Economic Modeling," Levine's Bibliography 843644000000000357, UCLA Department of Economics.
    13. Ani Guerdjikova & Jürgen Eichberger, 2023. "Cases and States ," Working Papers hal-03962412, HAL.
    14. Itzhak Gilboa, 2010. "Questions in Decision Theory," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 1-19, September.
    15. Gilboa, Itzhak & Schmeidler, David, 2010. "Simplicity and likelihood: An axiomatic approach," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1757-1775, September.
    16. repec:awi:wpaper:0470 is not listed on IDEAS
    17. Chiang, Mi-Hsiu & Chiu, Hsin-Yu & Kuo, Wei-Yu, 2021. "Predictive ability of similarity-based futures trading strategies," Pacific-Basin Finance Journal, Elsevier, vol. 68(C).
    18. Sharma, Tridib & Vadovic, Radovan, 2010. "Axiom of Monotonicity: An Experimental Test," MPRA Paper 22863, University Library of Munich, Germany.
    19. Bleile, Jörg, 2016. "Categorization based Belief formations," Center for Mathematical Economics Working Papers 519, Center for Mathematical Economics, Bielefeld University.
    20. Itzhak Gilboa & Andrew Postlewaite & Larry Samuelson & David Schmeidler, 2019. "What are axiomatizations good for?," Theory and Decision, Springer, vol. 86(3), pages 339-359, May.
    21. Chambers, Christopher P. & Hayashi, Takashi, 2010. "Bayesian consistent belief selection," Journal of Economic Theory, Elsevier, vol. 145(1), pages 432-439, January.

    More about this item

    Keywords

    Belief formation; prior; relative frequencies; case-based reasoning; similarity precision; ambiguity; learning; imagination; con dence; cautiousness.;
    All these keywords.

    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:bie:wpaper:507. 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: Bettina Weingarten (email available below). General contact details of provider: https://edirc.repec.org/data/imbiede.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.