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Symmetry of evidence without evidence of symmetry

Author

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  • Epstein, Larry G.

    () (Department of Economics, Boston University)

  • Seo, Kyoungwon

    () (Department of Managerial Economics and Decision Sciences, Northwestern University)

Abstract

The de Finetti Theorem is a cornerstone of the Bayesian approach. Bernardo (1996) writes that its "message is very clear: if a sequence of observations is judged to be exchangeable, then any subset of them must be regarded as a random sample from some model, and there exists a prior distribution on the parameter of such model, hence requiring a Bayesian approach." We argue that while exchangeability, interpreted as symmetry of evidence, is a weak assumption, when combined with subjective expected utility theory, it implies also complete confidence that experiments are identical. When evidence is sparse, and there is little evidence of symmetry, this implication of de Finetti's hypotheses is not intuitive. This motivates our adoption of multiple-priors utility as the benchmark model of preference. We provide two alternative generalizations of the de Finetti Theorem for this framework. A model of updating is also provided.

Suggested Citation

  • Epstein, Larry G. & Seo, Kyoungwon, 2010. "Symmetry of evidence without evidence of symmetry," Theoretical Economics, Econometric Society, vol. 5(3), September.
  • Handle: RePEc:the:publsh:596
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    References listed on IDEAS

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    1. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
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    Cited by:

    1. Epstein Larry G & Seo Kyoungwon, 2011. "Symmetry or Dynamic Consistency?," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-14, June.
    2. Epstein, Larry G. & Seo, Kyoungwon, 2014. "De Finetti meets Ellsberg," Research in Economics, Elsevier, vol. 68(1), pages 11-26.
    3. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2013. "Ambiguity and robust statistics," Journal of Economic Theory, Elsevier, vol. 148(3), pages 974-1049.
      • Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2011. "Ambiguity and Robust Statistics," Working Papers 382, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    4. Epstein, Larry G. & Halevy, Yoram, 2017. "Ambiguous Correlation," Microeconomics.ca working papers yoram_halevy-2017-2, Vancouver School of Economics, revised 09 Jan 2018.
    5. Peter Klibanoff & Sujoy Mukerji & Kyoungwon Seo, 2014. "Perceived Ambiguity and Relevant Measures," Econometrica, Econometric Society, vol. 82, pages 1945-1978, September.
    6. repec:bos:wpaper:wp2013-001 is not listed on IDEAS
    7. Luciano Castro & Alain Chateauneuf, 2011. "Ambiguity aversion and trade," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 243-273, October.
    8. Epstein, Larry G. & Seo, Kyoungwon, 2015. "Exchangeable capacities, parameters and incomplete theories," Journal of Economic Theory, Elsevier, vol. 157(C), pages 879-917.
    9. Nabil I. Al-Najjar & Luciano De Castro, 2010. "Prediction Markets to Forecast Electricity Demand," Discussion Papers 1529, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Roee Teper, 2016. "Plans of Action," Working Paper 5859, Department of Economics, University of Pittsburgh.
    11. Epstein, Larry G. & Halevy, Yoram, 2014. "No Two Experiments are Identical," Microeconomics.ca working papers yoram_halevy-2014-9, Vancouver School of Economics, revised 15 Feb 2017.
    12. Al-Najjar, Nabil I. & De Castro, Luciano, 2014. "Parametric representation of preferences," Journal of Economic Theory, Elsevier, vol. 150(C), pages 642-667.

    More about this item

    Keywords

    Ambiguity; exchangeability; symmetry; updating; learning; multiple-priors;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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