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Quantifying Information and Uncertainty

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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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    File URL: https://www.aeaweb.org/doi/10.1257/aer.20181897
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    Citations

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    Cited by:

    1. Corrao, Roberto & Fudenberg, Drew & Levine, David K., 2024. "On concave functions over lotteries," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    2. Hébert, Benjamin & Woodford, Michael, 2023. "Rational inattention when decisions take time," Journal of Economic Theory, Elsevier, vol. 208(C).
    3. Brice Corgnet & Simon Gaechter & Roberto Hernan Gonzalez, 2020. "Working Too Much for Too Little: Stochastic Rewards Cause Work Addiction," Discussion Papers 2020-03, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    4. Kubota,Megumi & Zeufack,Albert G., 2020. "Assessing the Returns on Investment in Data Openness and Transparency," Policy Research Working Paper Series 9139, The World Bank.
    5. Fissler, Tobias & Pesenti, Silvana M., 2023. "Sensitivity measures based on scoring functions," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1408-1423.
    6. J. Aislinn Bohren & Daniel N. Hauser, 2023. "Behavioral Foundations of Model Misspecification," PIER Working Paper Archive 23-007, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    7. Hou, Yunfei & Hu, Changsheng, 2023. "Understanding the role of aggregate analyst attention in resolving stock market uncertainty," Finance Research Letters, Elsevier, vol. 57(C).
    8. Tamer Boyaci, & Caner Canyakmaz, & Francis de Véricourt,, 2020. "Human and machine: The impact of machine input on decision-making under cognitive limitations," ESMT Research Working Papers ESMT-20-02, ESMT European School of Management and Technology.
    9. Daniele Pennesi, 2020. "Identity and information acquisition," Carlo Alberto Notebooks 610, Collegio Carlo Alberto, revised 2021.
    10. Avi Dor & William Encinosa & Kathleen Carey, 2020. "Hospital performance standards and medical pricing: The impact of information disclosure in cardiac care," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 29(3), pages 492-515, July.
    11. Luca Braghieri, 2023. "Biased Decoding and the Foundations of Communication," CESifo Working Paper Series 10432, CESifo.
    12. Mark Whitmeyer & Cole Williams, 2024. "Dynamic Signals," Papers 2407.16648, arXiv.org.
    13. Ehud Lehrer & Tao Wang, 2024. "The value of information in stopping problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(2), pages 619-648, September.
    14. Áron Tóbiás, 2023. "Cognitive limits and preferences for information," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 221-253, June.
    15. Benjamin Davies, 2024. "Learning about a changing state," Papers 2401.03607, arXiv.org.
    16. Ehud Lehrer & Tao Wang, 2022. "The Value of Information in Stopping Problems," Papers 2205.06583, arXiv.org.
    17. Brice Corgnet & Roberto Hernán González, 2023. "On The Appeal Of Complexity," Working Papers 2312, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    18. Roc Armenter & Michèle Müller-Itten & Zachary Stangebye, 2020. "Rational Inattention via Ignorance Equivalence," Working Papers 20-24, Federal Reserve Bank of Philadelphia.
    19. Daniele Pennesi, 2021. "Between Commitment and Flexibility: Revealing Anticipated Regret and Elation," Working papers 071, Department of Economics, Social Studies, Applied Mathematics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino.
    20. David Leong, 2024. "Mental Modeling of Entrepreneurial Opportunity Based on the Principle of Information Visualization," Business Perspectives and Research, , vol. 12(4), pages 488-504, October.

    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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