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Probabilities as Similarity-Weighted Frequencies

Author

Listed:
  • Itzhak Gilboa

    () (Tel Aviv University [Tel Aviv])

  • Antoine Billot

    (PJSE - Paris-Jourdan Sciences Economiques - ENS Paris - École normale supérieure - Paris - 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
    Note: View the original document on HAL open archive server: https://hal-hec.archives-ouvertes.fr/hal-00481235
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    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. Billot, Antoine & Gilboa, Itzhak & Schmeidler, David, 2008. "Axiomatization of an exponential similarity function," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 107-115, March.
    3. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2006. "Empirical Similarity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 433-444, August.
    4. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
    5. Antoine Billot & Itzhak Gilboa & David Schmeidler, 2004. "An Axiomatization of an Exponential Similarity Function," Levine's Bibliography 122247000000000678, UCLA Department of Economics.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Probability; similarity; case-based reasoning; relative frequencies;

    JEL classification:

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

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