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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
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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. 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)

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    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

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