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Information and the dispersion of posterior expectations

Author

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  • Brandt, Nikolai
  • Drees, Burkhard
  • Eckwert, Bernhard
  • Várdy, Felix

Abstract

We explore the intuitive idea that more information leads to greater dispersion of posterior beliefs about the expected state of the world. First, we show that two dispersion orders that have been widely used as informativeness criteria do not satisfy the desirable property of ordinality of states (OS), i.e., invariance to increasing monotone state transformations. Then, for the class of monotone information systems, we characterize the weakest information criteria that respect OS and imply the dispersion orders. Our characterizations consist of intuitive conditions on the joint distributions of signals and states. Because of OS, the information criteria induce the dispersion orders not only on the posterior expectations of states, but also of state utilities, under any strictly increasing vNM utility function.

Suggested Citation

  • Brandt, Nikolai & Drees, Burkhard & Eckwert, Bernhard & Várdy, Felix, 2014. "Information and the dispersion of posterior expectations," Journal of Economic Theory, Elsevier, vol. 154(C), pages 604-611.
    • Handle: RePEc:eee:jetheo:v:154:y:2014:i:c:p:604-611
    DOI: 10.1016/j.jet.2014.10.004
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    References listed on IDEAS

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    Cited by:

    1. Maxim Ivanov, 2021. "Optimal monotone signals in Bayesian persuasion mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(3), pages 955-1000, October.
    2. Bernhard Eckwert & Itzhak Zilcha, 2020. "The role of colleges within the higher education sector," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 315-336, March.
    3. Brandt, Nikolai M. & Eckwert, Bernhard & Várdy, Felix, 2021. "Bayesian learning with variable prior," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    4. Leoni, Patrick & Lundtofte, Frederik, 2017. "Information, stochastic dominance and bidding: The case of Treasury auctions," Economics Letters, Elsevier, vol. 153(C), pages 80-82.
    5. Marschak, Thomas & Shanthikumar, J. George & Zhou, Junjie, 2017. "Does more information-gathering effort raise or lower the average quantity produced?," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 104-117.

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    More about this item

    Keywords

    Information; Dispersion orderings; Decision making under uncertainty;
    All these keywords.

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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