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Perception of probabilities in situations of risk: A case based approach

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  • Gayer, Gabrielle
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    Abstract

    This paper provides a description of a possible mental process individuals go through in their attempt to comprehend stated probabilities in simple lotteries. The evaluation of probabilities is based on the following main components: lotteries encountered in the past, the realizations of these lotteries, and the similarity between stated probabilities. A probability is evaluated based on the experienced relative frequencies of outcomes that had that stated probability, as well as outcomes of other lotteries that had similar stated probabilities. This process may result in distortion of probabilities as observed in the literature, and in particular, in overvaluing low probabilities and undervaluing high probabilities. If the decision maker uses a less permissive similarity function as the size of memory grows, she will learn the real value of the stated probabilities. If, however, the similarity function is independent of memory, biases persist even when data are accumulated.

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    Bibliographic Info

    Article provided by Elsevier in its journal Games and Economic Behavior.

    Volume (Year): 68 (2010)
    Issue (Month): 1 (January)
    Pages: 130-143

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    Handle: RePEc:eee:gamebe:v:68:y:2010:i:1:p:130-143

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    Web page: http://www.elsevier.com/locate/inca/622836

    Related research

    Keywords: Distortion of probabilities Case based decision theory Similarity;

    References

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    1. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521586115.
    2. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-92, July.
    3. 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.
    4. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
    5. Gilboa, I. & Schmeidler, D., 2001. "Inductive Inference: An Axiomatic Approach," Papers 2001-19, Tel Aviv.
    6. Antoine Billot & Itzhak Gilboa & David Schmeidler, 2004. "Axiomatization of an Exponential Similarity Function," Cowles Foundation Discussion Papers 1485, Cowles Foundation for Research in Economics, Yale University.
    7. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    8. Rubinstein, Ariel, 1988. "Similarity and decision-making under risk (is there a utility theory resolution to the Allais paradox?)," Journal of Economic Theory, Elsevier, vol. 46(1), pages 145-153, October.
    9. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345.
    10. Antoine Billot & Itzhak Gilboa & David Schmeidler & Dov Samet, 2004. "Probabilities as Similarity-Weighted Frequencies," Cowles Foundation Discussion Papers 1492, Cowles Foundation for Research in Economics, Yale University.
    11. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2006. "Empirical Similarity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 433-444, August.
    12. Frederick Mosteller & Philip Nogee, 1951. "An Experimental Measurement of Utility," Journal of Political Economy, University of Chicago Press, vol. 59, pages 371.
    13. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    14. Guerdjikova, Ani, 2008. "Case-based learning with different similarity functions," Games and Economic Behavior, Elsevier, vol. 63(1), pages 107-132, May.
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    Cited by:
    1. Davide Marchiori & Sibilla Di Guida & Ido Erev, 2013. "Noisy retrievers and the four-fold reaction to rare events," Working Papers 3, Department of Management, Università Ca' Foscari Venezia.
    2. Aurélien Baillon & Laure Cabantous & Peter Wakker, 2012. "Aggregating imprecise or conflicting beliefs: An experimental investigation using modern ambiguity theories," Journal of Risk and Uncertainty, Springer, vol. 44(2), pages 115-147, April.

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