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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

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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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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  1. Edi Karni, 2009. "A Mechanism for Eliciting Probabilities," Econometrica, Econometric Society, vol. 77(2), pages 603-606, 03.
  2. 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.
  3. James E. Matheson & Robert L. Winkler, 1976. "Scoring Rules for Continuous Probability Distributions," Management Science, INFORMS, vol. 22(10), pages 1087-1096, June.
  4. repec:bla:restud:v:76:y:2009:i:4:p:1461-1489 is not listed on IDEAS
  5. Harrison, Glenn W. & Martínez-Correa, Jimmy & Swarthout, J. Todd, 2013. "Inducing risk neutral preferences with binary lotteries: A reconsideration," Journal of Economic Behavior & Organization, Elsevier, vol. 94(C), pages 145-159.
  6. 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.
  7. 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.
  8. Robert F. Nau, 2006. "Uncertainty Aversion with Second-Order Utilities and Probabilities," Management Science, INFORMS, vol. 52(1), pages 136-145, January.
  9. 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, 04.
  10. 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.
  11. Steffen Andersen & John Fountain & Glenn W. Harrison & E. Elisabet Rutström, 2010. "Estimating Subjective Probabilities," Experimental Economics Center Working Paper Series 2010-08, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University.
  12. Cox, James C & Oaxaca, Ronald L, 1995. "Inducing Risk-Neutral Preferences: Further Analysis of the Data," Journal of Risk and Uncertainty, Springer, vol. 11(1), pages 65-79, July.
  13. Reinhard Selten & Abdolkarim Sadrieh & Klaus Abbink, 1999. "Money Does Not Induce Risk Neutral Behavior, but Binary Lotteries Do even Worse," Theory and Decision, Springer, vol. 46(3), pages 213-252, June.
  14. 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.
  15. 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.
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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.
  2. Karl Schlag & James Tremewan & Joel van der Weele, 2014. "A Penny for Your Thoughts:A Survey of Methods for Eliciting Beliefs," Vienna Economics Papers 1401, University of Vienna, Department of Economics.

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