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Bayes Without Bernoulli: Simple Conditions for Probabilistic Choice

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Evolution and Progress in Democracies

Part of the book series: Theory and Decision Library ((TDLA,volume 31))

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Abstract

Anscombe and Aumann [1] demonstrated that introducing an objective randomizing device into the Savage setting of purely subjective uncertainty considerably simplifies the derivation of subjective probability from an individual’s preferences over uncertain bets. We present a more general derivation of classical subjective probability in this mixed subjective/objective setting, which neither assumes nor implies that risk preferences necessarily conform to the expected utility principle. We argue that the essence of “Bayesian rationality” is the assignment, correct manipulation, and proper updating of subjective event probabilities when evaluating and comparing uncertain prospects, regardless of whether attitudes toward risk satisfy the expected utility property. (Journal of Economic Literature Classification Numbers: D81, D84).

We are grateful to Ward Edwards, Peter Fishburn, Birgit Grodal, Edi Karni, David Kreps Duncan Luce, Michael Rothschild, Joel Sobel, Max Stinchcombe, an Associate Editor, and anonymous for helpful remarks on this material. Respomsinility for errors and opinions is our own.

Support from the National Science Founsation Economics Program and Decision, Risk and Management Science Program (Grant SES 92-09012) is gratefully acknowledged.

Part of this research has been done during a visit to the Center for Mathematical Studies in Economics and Management Science at Northwestern University.

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Author information

Authors and Affiliations

  1. Department of Economics, University of California-San Diego, 92093, La Jolla, California, USA

    Prof. Dr. Mark J. Machina

  2. Department of Economics, Ohio State University, 43210, Columbus, Ohio, USA

    Prof. Dr. David Schmeidler

Authors
  1. Prof. Dr. Mark J. Machina
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  2. Prof. Dr. David Schmeidler
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Editor information

Editors and Affiliations

  1. University of Graz, Austria

    Johann Götschl

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© 2001 Springer Science+Business Media Dordrecht

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Machina, M.J., Schmeidler, D. (2001). Bayes Without Bernoulli: Simple Conditions for Probabilistic Choice. In: Götschl, J. (eds) Evolution and Progress in Democracies. Theory and Decision Library, vol 31. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1504-1_9

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  • DOI: https://doi.org/10.1007/978-94-017-1504-1_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5842-3

  • Online ISBN: 978-94-017-1504-1

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