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Quantifying Information and Uncertainty

Author

Listed:
  • Alexander Frankel
  • Emir Kamenica

Abstract

We examine ways to measure the amount of information generated by a piece of news and the amount of uncertainty implicit in a given belief. Say a measure of information is valid if it corresponds to the value of news in some decision problem. Say a measure of uncertainty is valid if it corresponds to expected utility loss from not knowing the state in some decision problem. We axiomatically characterize all valid measures of information and uncertainty. We show that if measures of information and uncertainty arise from the same decision problem, then they are coupled in that the expected reduction in uncertainty always equals the expected amount of information generated. We provide explicit formulas for the measure of information that is coupled with any given measure of uncertainty and vice versa. Finally, we show that valid measures of information are the only payment schemes that never provide incentives to delay information revelation.

Suggested Citation

  • Alexander Frankel & Emir Kamenica, 2019. "Quantifying Information and Uncertainty," American Economic Review, American Economic Association, vol. 109(10), pages 3650-3680, October.
    • Handle: RePEc:aea:aecrev:v:109:y:2019:i:10:p:3650-80
    Note: DOI: 10.1257/aer.20181897
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    More about this item

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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