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Eliciting Beliefs: Proper Scoring Rules, Incentives, Stakes and Hedging

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  • Armantier, Olivier
  • Treich, Nicolas

Abstract

Accurate measurements of probabilistic beliefs have become increasingly important both in practice and in academia. Introduced by statisticians in the 1950s to promote truthful reports in simple environments, Proper Scoring Rules (PSR) are now arguably the most popular incentivized mechanisms to elicit an agent's beliefs. This paper generalizes the analysis of PSR to richer environments relevant to economists. More specifically, we combine theory and experiment to study how beliefs reported with a PSR may be biased when i) the PSR payments are increased, ii) the agent has a financial stake in the event she is predicting, and iii) the agent can hedge her prediction by taking an additional action. Our results reveal complex distortions of reported beliefs, thereby raising concerns about the ability of PSR to recover truthful beliefs in general economic environments.
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Suggested Citation

  • Armantier, Olivier & Treich, Nicolas, 2010. "Eliciting Beliefs: Proper Scoring Rules, Incentives, Stakes and Hedging," LERNA Working Papers 10.26.332, LERNA, University of Toulouse.
  • Handle: RePEc:ler:wpaper:10.26.332
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    1. Simon Gächter & Elke Renner, 2010. "The effects of (incentivized) belief elicitation in public goods experiments," Experimental Economics, Springer;Economic Science Association, vol. 13(3), pages 364-377, September.
    2. Alan S. Blinder & Michael Ehrmann & Marcel Fratzscher & Jakob De Haan & David-Jan Jansen, 2008. "Central Bank Communication and Monetary Policy: A Survey of Theory and Evidence," Journal of Economic Literature, American Economic Association, vol. 46(4), pages 910-945, December.
    3. Terrance Hurley & Jason Shogren, 2005. "An Experimental Comparison of Induced and Elicited Beliefs," Journal of Risk and Uncertainty, Springer, vol. 30(2), pages 169-188, January.
    4. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    5. Rutström, E. Elisabet & Wilcox, Nathaniel T., 2009. "Stated beliefs versus inferred beliefs: A methodological inquiry and experimental test," Games and Economic Behavior, Elsevier, vol. 67(2), pages 616-632, November.
    6. Jaffray, Jean-Yves & Karni, Edi, 1999. "Elicitation of Subjective Probabilities When the Initial Endowment is Unobservable," Journal of Risk and Uncertainty, Springer, vol. 18(1), pages 5-20, April.
    7. 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.
    8. Mariana Blanco & Dirk Engelmann & Alexander Koch & Hans-Theo Normann, 2010. "Belief elicitation in experiments: is there a hedging problem?," Experimental Economics, Springer;Economic Science Association, vol. 13(4), pages 412-438, December.
    9. 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.
    10. Huck, Steffen & Weizsacker, Georg, 2002. "Do players correctly estimate what others do? : Evidence of conservatism in beliefs," Journal of Economic Behavior & Organization, Elsevier, vol. 47(1), pages 71-85, January.
    11. Stefan T. Trautmann & Gijs Kuilen, 2015. "Belief Elicitation: A Horse Race among Truth Serums," Economic Journal, Royal Economic Society, vol. 125(589), pages 2116-2135, December.
    12. Davis, Douglas D. & Holt, Charles a., 1993. "Experimental economics: Methods, problems and promise," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 8(2), pages 179-212.
    13. Palfrey, Thomas R. & Wang, Stephanie W., 2009. "On eliciting beliefs in strategic games," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 98-109, August.
    14. Urs Fischbacher & Simon Gachter, 2010. "Social Preferences, Beliefs, and the Dynamics of Free Riding in Public Goods Experiments," American Economic Review, American Economic Association, vol. 100(1), pages 541-556, March.
    15. 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.
    16. Hans-Martin von Gaudecker & Arthur van Soest & Erik Wengstrom, 2011. "Heterogeneity in Risky Choice Behavior in a Broad Population," American Economic Review, American Economic Association, vol. 101(2), pages 664-694, April.
    17. Miguel A. Costa-Gomes & Georg Weizsäcker, 2008. "Stated Beliefs and Play in Normal-Form Games," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 729-762.
    18. Yaw Nyarko & Andrew Schotter, 2002. "An Experimental Study of Belief Learning Using Elicited Beliefs," Econometrica, Econometric Society, vol. 70(3), pages 971-1005, May.
    19. David Danz & Dietmar Fehr & Dorothea Kübler, 2012. "Information and beliefs in a repeated normal-form game," Experimental Economics, Springer;Economic Science Association, vol. 15(4), pages 622-640, December.
    20. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    21. Croson, Rachel T. A., 2000. "Thinking like a game theorist: factors affecting the frequency of equilibrium play," Journal of Economic Behavior & Organization, Elsevier, vol. 41(3), pages 299-314, March.
    22. Edi Karni, 2009. "A Mechanism for Eliciting Probabilities," Econometrica, Econometric Society, vol. 77(2), pages 603-606, March.
    23. Yoram Halevy, 2007. "Ellsberg Revisited: An Experimental Study," Econometrica, Econometric Society, vol. 75(2), pages 503-536, March.
    24. Osband, Kent, 1989. "Optimal Forecasting Incentives," Journal of Political Economy, University of Chicago Press, vol. 97(5), pages 1091-1112, October.
    25. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    26. Charles F. Manski, 2004. "Measuring Expectations," Econometrica, Econometric Society, vol. 72(5), pages 1329-1376, September.
    27. McKelvey, Richard D & Page, Talbot, 1990. "Public and Private Information: An Experimental Study of Information Pooling," Econometrica, Econometric Society, vol. 58(6), pages 1321-1339, November.
    28. Karni, Edi, 1999. "Elicitation of Subjective Probabilities When Preferences Are State-Dependent," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 479-486, May.
    29. repec:pri:cepsud:161blinder is not listed on IDEAS
    30. Charles N. Noussair & Stefan T. Trautmann & Gijs van de Kuilen, 2014. "Higher Order Risk Attitudes, Demographics, and Financial Decisions," Review of Economic Studies, Oxford University Press, vol. 81(1), pages 325-355.
    31. Franklin Allen, 1987. "Notes--Discovering Personal Probabilities When Utility Functions are Unknown," Management Science, INFORMS, vol. 33(4), pages 542-544, April.
    32. 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.
    33. Armantier, Olivier & Boly, Amadou, 2011. "A controlled field experiment on corruption," European Economic Review, Elsevier, vol. 55(8), pages 1072-1082.
    34. Ledyard, John & Hanson, Robin & Ishikida, Takashi, 2009. "An experimental test of combinatorial information markets," Journal of Economic Behavior & Organization, Elsevier, vol. 69(2), pages 182-189, February.
    35. Marco Ottaviani & Peter Norman Sørensen, 2007. "Outcome Manipulation in Corporate Prediction Markets," Journal of the European Economic Association, MIT Press, vol. 5(2-3), pages 554-563, 04-05.
    36. Manski, Charles F., 2002. "Identification of decision rules in experiments on simple games of proposal and response," European Economic Review, Elsevier, vol. 46(4-5), pages 880-891, May.
    37. Michael Abramowicz, 2007. "The Hidden Beauty of the Quadratic Market Scoring Rule: A Uniform Liquidity Market Maker, with Variations," Journal of Prediction Markets, University of Buckingham Press, vol. 1(2), pages 111-125, July.
    38. Daniel Read, 2005. "Monetary incentives, what are they good for?," Journal of Economic Methodology, Taylor & Francis Journals, vol. 12(2), pages 265-276.
    39. Olivier Armantier & Nicolas Treich, 2009. "Subjective Probabilities In Games: An Application To The Overbidding Puzzle," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 50(4), pages 1079-1102, November.
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    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior

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