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Cognitive Imprecision and Stake-Dependent Risk Attitudes

Author

Listed:
  • Mel Win Khaw
  • Ziang Li
  • Michael Woodford

Abstract

In an experiment that elicits subjects’ willingness to pay (WTP) for the outcome of a lottery, we confirm the fourfold pattern of risk attitudes described by Kahneman and Tversky. In addition, we document a systematic effect of stake sizes on the magnitude and sign of the relative risk premium, holding fixed both the probability that a lottery pays off and the sign of its payoff (gain vs. loss). We further show that in our data, there is a log-linear relationship between the monetary payoff of the lottery and WTP, conditional on the probability of the payoff and its sign. We account quantitatively for this relationship, and the way in which it varies with both the probability and sign of the lottery payoff, in a model in which all departures from risk-neutral bidding are attributed to an optimal adaptation of bidding behaviour to the presence of cognitive noise. Moreover, the cognitive noise required by our hypothesis is consistent with patterns of bias and variability in judgments about numerical magnitudes and probabilities that have been observed in other contexts.

Suggested Citation

  • Mel Win Khaw & Ziang Li & Michael Woodford, 2022. "Cognitive Imprecision and Stake-Dependent Risk Attitudes," CESifo Working Paper Series 9923, CESifo.
    • Handle: RePEc:ces:ceswps:_9923
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    File URL: https://www.cesifo.org/DocDL/cesifo1_wp9923.pdf
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    References listed on IDEAS

    as
    1. Khaw, Mel Win & Stevens, Luminita & Woodford, Michael, 2017. "Discrete adjustment to a changing environment: Experimental evidence," Journal of Monetary Economics, Elsevier, vol. 91(C), pages 88-103.
    2. Benjamin Enke & Thomas W. Graeber, 2021. "Cognitive Uncertainty in Intertemporal Choice," CESifo Working Paper Series 9472, CESifo.
    3. Ned Augenblick & Eben Lazarus & Michael Thaler, 2021. "Overinference from Weak Signals and Underinference from Strong Signals," Papers 2109.09871, arXiv.org, revised Jun 2024.
    4. Carlos Alós-Ferrer & Ernst Fehr & Nick Netzer, 2021. "Time Will Tell: Recovering Preferences When Choices Are Noisy," Journal of Political Economy, University of Chicago Press, vol. 129(6), pages 1828-1877.
    5. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    6. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    7. Michael Woodford, 2020. "Modeling Imprecision in Perception, Valuation, and Choice," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 579-601, August.
    8. Benjamin Enke & Thomas Graeber, 2021. "Cognitive Uncertainty in Intertemporal Choice," NBER Working Papers 29577, National Bureau of Economic Research, Inc.
    9. Paulo Natenzon, 2019. "Random Choice and Learning," Journal of Political Economy, University of Chicago Press, vol. 127(1), pages 419-457.
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    12. Kachelmeier, Steven J & Shehata, Mohamed, 1992. "Examining Risk Preferences under High Monetary Incentives: Experimental Evidence from the People's Republic of China," American Economic Review, American Economic Association, vol. 82(5), pages 1120-1141, December.
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    More about this item

    Keywords

    prospect theory; fourfold pattern; endogenous precision; cognitive noise;
    All these keywords.

    JEL classification:

    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D87 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Neuroeconomics

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