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Scoring Rules for Subjective Probability Distributions

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  • Glenn W. Harrison
  • Jimmy Martínez-Correa
  • J. Todd Swarthout
  • Eric R. Ulm
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    Abstract

    The theoretical literature has a rich characterization of scoring rules for eliciting the subjective beliefs that an individual has for continuous events, but under the restrictive assumption of risk neutrality. It is well known that risk aversion can dramatically affect the incentives to correctly report the true subjective probability of a binary event. Alternatively, one must carefully calibrate inferences about true subjective probabilities from elicited subjective probabilities over binary events, recognizing the incentives that risk averse agents have to report the same probability for the two outcomes and reduce the variability of payoffs from the scoring rule. We characterize the comparable implications of the general case of a risk averse agent when facing a popular scoring rule over continuous events, and find that these concerns do not apply with anything like the same force. For empirically plausible levels of risk aversion, one can reliably elicit most important features of the latent subjective belief distribution without undertaking calibration for risk attitudes.

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    File URL: http://excen.gsu.edu/workingpapers/GSU_EXCEN_WP_2012-18.pdf
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    Bibliographic Info

    Paper provided by Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University in its series Experimental Economics Center Working Paper Series with number 2012-18.

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    Length: 26
    Date of creation: Nov 2012
    Date of revision:
    Handle: RePEc:exc:wpaper:2012-18

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    References

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    1. Glenn W. Harrison & J. Todd Swarthout, 2012. "The Independence Axiom and the Bipolar Behaviorist," Experimental Economics Center Working Paper Series 2012-01, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University.
    2. Andersen, Steffen & Fountain, John & Harrison, Glenn W. & Rutström, Elisabet E., 2009. "Estimating Subjective Probabilities," Working Papers 05-2009, Copenhagen Business School, Department of Economics.
    3. Theo Offerman & Joep Sonnemans & Gijs Van De Kuilen & Peter P. Wakker, 2009. "A Truth Serum for Non-Bayesians: Correcting Proper Scoring Rules for Risk Attitudes ," Review of Economic Studies, Oxford University Press, vol. 76(4), pages 1461-1489.
    4. Edi Karni, 2009. "A Mechanism for Eliciting Probabilities," Econometrica, Econometric Society, vol. 77(2), pages 603-606, 03.
    5. repec:bla:restud:v:76:y:2009:i:4:p:1461-1489 is not listed on IDEAS
    6. Delavande, Adeline & Gine, Xavier & McKenzie, David, 2009. "Measuring Subjective Expectations in Developing Countries: A Critical Review and New Evidence," Policy Research Working Paper Series 4824, The World Bank.
    7. Grether, David M., 1992. "Testing bayes rule and the representativeness heuristic: Some experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 17(1), pages 31-57, January.
    8. Robert F. Nau, 2006. "Uncertainty Aversion with Second-Order Utilities and Probabilities," Management Science, INFORMS, vol. 52(1), pages 136-145, January.
    9. James E. Matheson & Robert L. Winkler, 1976. "Scoring Rules for Continuous Probability Distributions," Management Science, INFORMS, vol. 22(10), pages 1087-1096, June.
    10. Holt, Charles A. & Smith, Angela M., 2009. "An update on Bayesian updating," Journal of Economic Behavior & Organization, Elsevier, vol. 69(2), pages 125-134, February.
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    Cited by:
    1. Jaspersen, Johannes G., 2013. "An incentive compatible scoring rule for ordinal judgments of expected utility maximizers," Economics Letters, Elsevier, vol. 120(2), pages 245-248.

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