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A True Expert Knows which Question Should Be Asked

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  • Feinberg, Yossi

    (Stanford U)

  • Dekel, Eddie

    (Northwestern U)

Abstract

We suggest a test for discovering whether a potential expert is informed of the distribution of a stochastic process. In a non-Bayesian non-parametric setting, the expert is asked to make a prediction which is tested against a single realization of the stochastic process. It is shown that by asking the expert to predict a "small" set of sequences, the test will assure that any informed expert can pass the test with probability one with respect to the actual distribution. Moreover, for the uninformed non-expert it is impossible to pass this test, in the sense that for any choice of a "small" set of sequences, only a "small" set of measures will assign a positive probability to the given set. Hence for "most" measures, the non-expert will surely fail the test. We define small as category 1 sets, described in more detail in the paper.

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Bibliographic Info

Paper provided by Stanford University, Graduate School of Business in its series Research Papers with number 1856.

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Date of creation: Jun 2004
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Handle: RePEc:ecl:stabus:1856

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  1. Ehud Kalai & Ehud Lehrer & Rann Smorodinsky, 2010. "Calibrated Forecasting and Merging," Levine's Working Paper Archive 584, David K. Levine.
  2. Fudenberg, Drew & Levine, David, 1995. "Consistency and Cautious Fictitious Play," Scholarly Articles 3198694, Harvard University Department of Economics.
  3. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 40-55, October.
  4. Drew Fudenberg & David K. Levine, 1997. "Conditional Universal Consistency," Levine's Working Paper Archive 471, David K. Levine.
  5. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
  6. Sergiu Hart & Andreu Mas-Colell, 1999. "A general class of adaptative strategies," Economics Working Papers 373, Department of Economics and Business, Universitat Pompeu Fabra.
  7. Sandroni, Alvaro & Smorodinsky, Rann, 2004. "Belief-based equilibrium," Games and Economic Behavior, Elsevier, vol. 47(1), pages 157-171, April.
  8. Alvaro Sandroni, 2003. "The reproducible properties of correct forecasts," International Journal of Game Theory, Springer, vol. 32(1), pages 151-159, December.
  9. Lehrer, Ehud, 2001. "Any Inspection Is Manipulable," Econometrica, Econometric Society, vol. 69(5), pages 1333-47, September.
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