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Probabilities as Similarity-Weighted Frequencies

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  • Antoine Billot

    (Universite de Paris II)

  • Itzhak Gilboa

    (School of Economics, Tel Aviv University)

  • David Schmeidler

    (School of Mathematical Sciences, Tel Aviv Univ.)

  • Dov Samet

    (Tel Aviv University)

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.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1492.

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Length: 20 pages
Date of creation: Nov 2004
Date of revision:
Publication status: Published in Econometrica (2005), 73: 1125-1136
Handle: RePEc:cwl:cwldpp:1492

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Keywords: Similarity; Probability;

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  1. Gilboa, I. & Schmeidler, D., 1999. "Inductive Inference: an Axiomatic Approach," Papers 29-99, Tel Aviv.
  2. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2006. "Empirical Similarity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 433-444, August.
  3. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  4. Antoine Billot & Itzhak Gilboa & David Schmeidler, 2004. "An Axiomatization of an Exponential Similarity Function," Levine's Bibliography 122247000000000678, UCLA Department of Economics.
  5. Antoine Billot & Itzhak Gilboa & David Schmeidler, 2004. "Axiomatization of an Exponential Similarity Function," Cowles Foundation Discussion Papers 1485, Cowles Foundation for Research in Economics, Yale University.
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