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Probabilities as Similarity-Weighted Frequencies

Author

Listed:
  • Antoine Billot
  • Itzhak Gilboa
  • 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. Copyright The Econometric Society 2005.

Suggested Citation

  • Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2005. "Probabilities as Similarity-Weighted Frequencies," Econometrica, Econometric Society, vol. 73(4), pages 1125-1136, July.
  • Handle: RePEc:ecm:emetrp:v:73:y:2005:i:4:p:1125-1136
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    File URL: http://hdl.handle.net/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. 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.
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    Citations

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    Cited by:

    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, 2010. "Questions in Decision Theory," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 1-19, September.
    3. Eichberger, Jurgen & Guerdjikova, Ani, 2007. "Multiple Priors as Similarity Weighted Frequencies," Working Papers 07-03, Cornell University, Center for Analytic Economics.
    4. Rossella Argenziano & Itzhak Gilboa, 2012. "History as a coordination device," Theory and Decision, Springer, vol. 73(4), pages 501-512, October.
    5. Eichberger, Jürgen & Guerdjikova, Ani, 2010. "Case-based belief formation under ambiguity," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 161-177, November.
    6. Steiner, Jakub & Stewart, Colin, 2008. "Contagion through learning," Theoretical Economics, Econometric Society, vol. 3(4), December.
    7. Gilboa, Itzhak & Schmeidler, David, 2010. "Simplicity and likelihood: An axiomatic approach," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1757-1775, September.
    8. Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2007. "Probabilities in Economic Modeling," PIER Working Paper Archive 07-023, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    9. Billot, Antoine & Gilboa, Itzhak & Schmeidler, David, 2008. "Axiomatization of an exponential similarity function," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 107-115, March.
    10. 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.
    11. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2007. "On the Definition of Objective Probabilities by Empirical Similarity," Levine's Bibliography 843644000000000363, UCLA Department of Economics.
    12. 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.
    13. Eichberger, Jürgen & Guerdjikova, Ani, 2008. "Multiple Priors as Similarity Weighted Frequencies," Papers 08-07, Sonderforschungsbreich 504.
    14. Pauline Barrieu & Sinclair Desgagn�, 2009. "Economic policy when models disagree," GRI Working Papers 4, Grantham Research Institute on Climate Change and the Environment.
    15. repec:the:publsh:2653 is not listed on IDEAS
    16. Pe[combining cedilla]ski, Marcin, 2011. "Prior symmetry, similarity-based reasoning, and endogenous categorization," Journal of Economic Theory, Elsevier, vol. 146(1), pages 111-140, January.
    17. Jakub Steiner & Colin Stewart, 2007. "Learning by Similarity in Coordination Problems," CERGE-EI Working Papers wp324, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    18. Pauline Barrieu & Bernard Sinclair-Desgagné, 2009. "Economic Policy when Models Disagree," CIRANO Working Papers 2009s-03, CIRANO.
    19. Golosnoy, Vasyl & Okhrin, Yarema, 2008. "General uncertainty in portfolio selection: A case-based decision approach," Journal of Economic Behavior & Organization, Elsevier, vol. 67(3-4), pages 718-734, September.
    20. Teitelbaum, Joshua C., 2013. "Asymmetric empirical similarity," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 346-351.
    21. Bleile, Jörg, 2016. "Limited Attention in Case-Based Belief Formation," Center for Mathematical Economics Working Papers 518, Center for Mathematical Economics, Bielefeld University.
    22. Bleile, Jörg, 2016. "Categorization based Belief formations," Center for Mathematical Economics Working Papers 519, Center for Mathematical Economics, Bielefeld University.
    23. 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.
    24. Bleile, Jörg, 2016. "Cautious Belief Formation," Center for Mathematical Economics Working Papers 507, Center for Mathematical Economics, Bielefeld University.

    More about this item

    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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