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Scoring Rules for Subjective Probability Distributions

Listed author(s):
  • Glenn W. Harrison
  • Jimmy Martínez-Correa
  • J. Todd Swarthout
  • Eric R. Ulm

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
File Function: First version, 2012
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File URL: http://excen.gsu.edu/workingpapers/GSU_EXCEN_WP_2013-05.pdf
File Function: Revised version, 2013
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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: Apr 2013
Handle: RePEc:exc:wpaper:2012-18
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  1. Armantier, Olivier & Treich, Nicolas, 2013. "Eliciting beliefs: Proper scoring rules, incentives, stakes and hedging," European Economic Review, Elsevier, vol. 62(C), pages 17-40.
  2. Steffen Andersen & John Fountain & Glenn Harrison & E. Rutström, 2014. "Estimating subjective probabilities," Journal of Risk and Uncertainty, Springer, vol. 48(3), pages 207-229, June.
  3. Constantinos Antoniou & Glenn Harrison & Morten Lau & Daniel Read, 2015. "Subjective Bayesian beliefs," Journal of Risk and Uncertainty, Springer, vol. 50(1), pages 35-54, February.
  4. Kenneth C. Lichtendahl, Jr. & Robert L. Winkler, 2007. "Probability Elicitation, Scoring Rules, and Competition Among Forecasters," Management Science, INFORMS, vol. 53(11), pages 1745-1755, November.
  5. Jeff Dominitz & Charles F. Manski, 2011. "Measuring and interpreting expectations of equity returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(3), pages 352-370, April.
  6. James E. Matheson & Robert L. Winkler, 1976. "Scoring Rules for Continuous Probability Distributions," Management Science, INFORMS, vol. 22(10), pages 1087-1096, June.
  7. Harrison, Glenn W. & Martínez-Correa, Jimmy & Swarthout, J. Todd, 2015. "Reduction of compound lotteries with objective probabilities: Theory and evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 119(C), pages 32-55.
  8. 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.
  9. 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.
  10. Glenn W. Harrison & Jia Min Ng, 2016. "Evaluating The Expected Welfare Gain From Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(1), pages 91-120, 01.
  11. Harrison, Glenn W. & Martínez-Correa, Jimmy & Swarthout, J. Todd, 2014. "Eliciting subjective probabilities with binary lotteries," Journal of Economic Behavior & Organization, Elsevier, vol. 101(C), pages 128-140.
  12. Edi Karni, 2009. "A Mechanism for Eliciting Probabilities," Econometrica, Econometric Society, vol. 77(2), pages 603-606, March.
  13. Charles A. Holt & Susan K. Laury, 2005. "Risk Aversion and Incentive Effects: New Data without Order Effects," American Economic Review, American Economic Association, vol. 95(3), pages 902-912, June.
  14. Robert F. Nau, 2006. "Uncertainty Aversion with Second-Order Utilities and Probabilities," Management Science, INFORMS, vol. 52(1), pages 136-145, January.
  15. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
  16. 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.
  17. 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.
  18. Costa-Gomes, Miguel A. & Huck, Steffen & Weizsäcker, Georg, 2014. "Beliefs and actions in the trust game: Creating instrumental variables to estimate the causal effect," Games and Economic Behavior, Elsevier, vol. 88(C), pages 298-309.
  19. Merkle, Christoph & Weber, Martin, 2011. "True overconfidence: The inability of rational information processing to account for apparent overconfidence," Organizational Behavior and Human Decision Processes, Elsevier, vol. 116(2), pages 262-271.
  20. repec:cup:jfinqa:v:52:y:2017:i:02:p:737-750_00 is not listed on IDEAS
  21. Ergin, Haluk & Gul, Faruk, 2009. "A theory of subjective compound lotteries," Journal of Economic Theory, Elsevier, vol. 144(3), pages 899-929, May.
  22. Antoniou, Constantinos & Harrison, Glenn W. & Lau, Morten I. & Read, Daniel, 2017. "Information Characteristics and Errors in Expectations: Experimental Evidence," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 52(02), pages 737-750, April.
  23. Delavande, Adeline & Giné, Xavier & McKenzie, David, 2011. "Measuring subjective expectations in developing countries: A critical review and new evidence," Journal of Development Economics, Elsevier, vol. 94(2), pages 151-163, March.
  24. Offerman, Theo & Sonnemans, Joep & Schram, Arthur, 1996. "Value Orientations, Expectations and Voluntary Contributions in Public Goods," Economic Journal, Royal Economic Society, vol. 106(437), pages 817-845, July.
  25. Fiore, Stephen M. & Harrison, Glenn W. & Hughes, Charles E. & Rutstrm, E. Elisabet, 2009. "Virtual experiments and environmental policy," Journal of Environmental Economics and Management, Elsevier, vol. 57(1), pages 65-86, January.
  26. Glenn Harrison & J. Swarthout, 2014. "Experimental payment protocols and the Bipolar Behaviorist," Theory and Decision, Springer, vol. 77(3), pages 423-438, October.
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