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Efficient interval scoring rules

Author

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  • Karl Schlag
  • Joël van der Weele

Abstract

Scoring rules that elicit an entire belief distribution through the elicitation of point beliefs are time-consuming and demand considerable cognitive e¤ort. Moreover, the results are valid only when agents are risk-neutral or when one uses probabilistic rules. We investigate a class of rules in which the agent has to choose an interval and is rewarded (deterministically) on the basis of the chosen interval and the realization of the random variable. We formulate an e¢ ciency criterion for such rules and present a speci.c interval scoring rule. For single- peaked beliefs, our rule gives information about both the location and the dispersion of the belief distribution. These results hold for all concave utility functions.

Suggested Citation

  • Karl Schlag & Joël van der Weele, 2009. "Efficient interval scoring rules," Economics Working Papers 1176, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:1176
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    References listed on IDEAS

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    1. Roberto Galbiati & Karl Schlag & Joël van der Weele, 2009. "Can sanctions induce pessimism? An experiment," Economics Working Papers 1150, Department of Economics and Business, Universitat Pompeu Fabra.
    2. 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.
    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 ," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(4), pages 1461-1489.
    4. Schmalensee, Richard, 1976. "An Experimental Study of Expectation Formation," Econometrica, Econometric Society, vol. 44(1), pages 17-41, January.
    5. Andersen, Steffen & Fountain, John & Harrison, Glenn W. & Rutström, Elisabet, 2009. "Eliciting Beliefs," Working Papers 03-2009, Copenhagen Business School, Department of Economics.
    6. Dufwenberg, Martin & Gneezy, Uri, 2000. "Measuring Beliefs in an Experimental Lost Wallet Game," Games and Economic Behavior, Elsevier, vol. 30(2), pages 163-182, February.
    7. 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.
    8. 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.
    9. Rutstrom, E. Elizabet & Wilcox, Nathaniel, 2008. "Stated versus inferred beliefs: A methodological inquiry and experimental test," MPRA Paper 11852, University Library of Munich, Germany.
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    Citations

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    Cited by:

    1. Galbiati, Roberto & Schlag, Karl H. & van der Weele, Joël J., 2013. "Sanctions that signal: An experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 94(C), pages 34-51.
    2. Franziska Tausch & Jan Potters & Arno Riedl, 2014. "An experimental investigation of risk sharing and adverse selection," Journal of Risk and Uncertainty, Springer, vol. 48(2), pages 167-186, April.
    3. Elena Cettolin & Arno Riedl, 2017. "Justice Under Uncertainty," Management Science, INFORMS, vol. 63(11), pages 3739-3759, November.
    4. Elena Cettolin & Arno Riedl, 2011. "Partial Coercion, Conditional Cooperation, and Self-Commitment in Voluntary Contributions to Public Goods," CESifo Working Paper Series 3556, CESifo.
    5. Ronald Peeters & Leonard Wolk, 2017. "Eliciting interval beliefs: An experimental study," PLOS ONE, Public Library of Science, vol. 12(4), pages 1-15, April.
    6. Blume, Andreas & Lai, Ernest K. & Lim, Wooyoung, 2019. "Eliciting private information with noise: The case of randomized response," Games and Economic Behavior, Elsevier, vol. 113(C), pages 356-380.
    7. Galbiati, Roberto & Schlag, Karl H. & van der Weele, Joël J., 2013. "Sanctions that signal: An experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 94(C), pages 34-51.
    8. Peeters, Ronald & Vorsatz, Marc & Walzl, Markus, 2015. "Beliefs and truth-telling: A laboratory experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 113(C), pages 1-12.
    9. Michał Krawczyk, 2011. "Overconfident for real? Proper scoring for confidence intervals," Working Papers 2011-15, Faculty of Economic Sciences, University of Warsaw.
    10. Peeters, Ronald & Vorsatz, Marc, 2021. "Simple guilt and cooperation," Journal of Economic Psychology, Elsevier, vol. 82(C).
    11. Peeters, R.J.A.P. & Wolk, K.L., 2014. "Eliciting and aggregating individual expectations: An experimental study," Research Memorandum 029, Maastricht University, Graduate School of Business and Economics (GSBE).

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    More about this item

    Keywords

    Belief elicitation; scoring rules; subjective probabilities;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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