IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-00481235.html
   My bibliography  Save this paper

Probabilities as Similarity-Weighted Frequencies

Author

Listed:
  • Itzhak Gilboa

    (TAU - Tel Aviv University)

  • Antoine Billot

    (PJSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, LEM - Laboratoire d'Économie Moderne - UP2 - Université Panthéon-Assas)

  • Dov Samet
  • David Schmeidler

Abstract

A decision maker is asked to express her beliefs by assigning probabilities to certain possible states. We focus on the relationship between her database and her beliefs. We show that, if beliefs given a union of two databases are a convex combination of beliefs given each of the databases, the belief formation process follows a simple formula: beliefs are a similarity-weighted average of the beliefs induced by each past case.

Suggested Citation

  • Itzhak Gilboa & Antoine Billot & Dov Samet & David Schmeidler, 2005. "Probabilities as Similarity-Weighted Frequencies," Post-Print hal-00481235, HAL.
    • Handle: RePEc:hal:journl:hal-00481235
    DOI: 10.1111/j.1468-0262.2005.00611.x
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    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. 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..
    3. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-1092, July.
    4. 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..
    5. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
    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. 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.
    2. Gilboa, Itzhak & Lieberman, Offer & Schmeidler, David, 2011. "A similarity-based approach to prediction," Journal of Econometrics, Elsevier, vol. 162(1), pages 124-131, May.
    3. Bleile, Jörg, 2016. "Cautious Belief Formation," Center for Mathematical Economics Working Papers 507, Center for Mathematical Economics, Bielefeld University.
    4. 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..
    5. R. Luce & A. Marley, 2005. "Ranked Additive Utility Representations of Gambles: Old and New Axiomatizations," Journal of Risk and Uncertainty, Springer, vol. 30(1), pages 21-62, January.
    6. Golosnoy, Vasyl & Hamid, Alain & Okhrin, Yarema, 2014. "The empirical similarity approach for volatility prediction," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 321-329.
    7. Mongin, Philippe & Pivato, Marcus, 2015. "Ranking multidimensional alternatives and uncertain prospects," Journal of Economic Theory, Elsevier, vol. 157(C), pages 146-171.
    8. 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..
    9. Itzhak Gilboa, 2010. "Questions in Decision Theory," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 1-19, September.
    10. Gilboa, Itzhak & Schmeidler, David & Wakker, Peter P., 2002. "Utility in Case-Based Decision Theory," Journal of Economic Theory, Elsevier, vol. 105(2), pages 483-502, August.
    11. 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.
    12. Mohlin, Erik, 2014. "Optimal categorization," Journal of Economic Theory, Elsevier, vol. 152(C), pages 356-381.
    13. Gilboa, Itzhak & Schmeidler, David, 2010. "Simplicity and likelihood: An axiomatic approach," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1757-1775, September.
    14. Henry, Marc, 2007. "A representation of decision by analogy," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 771-794, September.
    15. Stoye, Jörg, 2011. "Axioms for minimax regret choice correspondences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2226-2251.
    16. Teitelbaum, Joshua C., 2013. "Asymmetric empirical similarity," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 346-351.
    17. Charness, Gary & Levin, Dan & Schmeidler, David, 2019. "An experimental study of estimation and bidding in common-value auctions with public information," Journal of Economic Theory, Elsevier, vol. 179(C), pages 73-98.
    18. 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.
    19. Itzhak Gilboa & Andrew Postlewaite & Larry Samuelson & David Schmeidler, 2011. "Economic Models as Analogies," PIER Working Paper Archive 12-001, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    20. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.

    More about this item

    Keywords

    Probability; similarity; case-based reasoning; relative frequencies;
    All these keywords.

    JEL classification:

    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

    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:hal:journl:hal-00481235. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.