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Asymmetry of Risk and Value of Information

Listed author(s):
  • Roman V. Belavkin

    (Middlesex University London)

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    The von Neumann and Morgenstern theory postulates that rational choice under uncertainty is equivalent to maximization of expected utility (EU). This view is mathematically appealing and natural because of the affine structure of the space of probability measures. Behavioural economists and psychologists, on the other hand, have demonstrated that humans consistently violate the EU postulate by switching from risk-averse to risk-taking behaviour. This paradox has led to the development of descriptive theories of decisions, such as the celebrated prospect theory, which uses an S-shaped value function with concave and convex branches explaining the observed asymmetry. Although successful in modelling human behaviour, these theories appear to contradict the natural set of axioms behind the EU postulate. Here we show that the observed asymmetry in behaviour can be explained if, apart from utilities of the out comes, rational agents also value information communicated by random events. We review the main ideas of the classical value of information theory and its generalizations. Then we prove that the value of information is an S-shaped function, and that its asymmetry does not depend on how the concept of information is defined, but follows only from linearity of the expected utility. Thus, unlike many descriptive and `non-expected' utility theories that abandon the linearity (i.e. the `independence' axiom), we formulate a rigorous argument that the von Neumann and Morgenstern rational agents should be both risk-averse and risk-taking if they are not indifferen to information.

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    File URL: http://repeck.bilgi.edu.tr/RePEc/beb/wpseet/BelisWP_SEET03.pdf
    File Function: First version, 2014
    Download Restriction: no

    Paper provided by BELIS, Istanbul Bilgi University in its series SEET Working Papers with number 2014-03.

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    Length: 17 pages
    Date of creation: Jun 2014
    Handle: RePEc:beb:wpseet:201403
    Contact details of provider: Web page: http://belis.bilgi.edu.tr
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    1. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
    2. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    3. Roman Belavkin, 2013. "Optimal measures and Markov transition kernels," Journal of Global Optimization, Springer, vol. 55(2), pages 387-416, February.
    4. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    5. Loomes, Graham & Sugden, Robert, 1982. "Regret Theory: An Alternative Theory of Rational Choice under Uncertainty," Economic Journal, Royal Economic Society, vol. 92(368), pages 805-824, December.
    6. Steffen Huck & Wieland Müller, 2012. "Allais for all: Revisiting the paradox in a large representative sample," Journal of Risk and Uncertainty, Springer, vol. 44(3), pages 261-293, June.
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