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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 speci cally, 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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Paper provided by Institut d'Économie Industrielle (IDEI), Toulouse in its series IDEI Working Papers with number 643.

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Date of creation: 15 Apr 2010
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Publication status: Published in European Economic Review, vol.�62, Elsevier, 2013, p.�17-40.
Handle: RePEc:ide:wpaper:23504

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Cited by:
  1. Dreber, Anna & Ellingsen, Tore & Johannesson, Magnus & Rand, David, 2011. "Do People Care about Social Context? Framing Effects in Dictator Games," Working Paper Series in Economics and Finance 738, Stockholm School of Economics.
  2. Manski, Charles F. & Neri, Claudia, 2013. "First- and second-order subjective expectations in strategic decision-making: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 232-254.
  3. Olivier Armantier & Scott Nelson & Giorgio Topa & Wilbert van der Klaauw & Basit Zafar, 2012. "The price is right: updating of inflation expectations in a randomized price information experiment," Staff Reports 543, Federal Reserve Bank of New York.
  4. Federica Alberti & Anna Conte & Kei Tsutsui, 2014. "Accuracy of proposers' beliefs in an allocation-type game," Jena Economic Research Papers 2014-002, Friedrich-Schiller-University Jena, Max-Planck-Institute of Economics.
  5. Guy Mayraz, 2011. "Wishful Thinking," CEP Discussion Papers dp1092, Centre for Economic Performance, LSE.
  6. Matthew Wiswall & Basit Zafar, 2011. "Belief updating among college students: evidence from experimental variation in information," Staff Reports 516, Federal Reserve Bank of New York.

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