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R. Winkler and A. Murphy, “Nonlinear Utility and the Probability Score,” Journal of Applied Meteorology, Vol. 9, 1970, pp. 143-148. doi:10.1175/1520-0450(1970)009<0143:NUATPS>2.0.CO;2

has been cited by the following article:

• TITLE: Eliciting Probabilities, Means, Medians, Variances and Covariances without Assuming Risk Neutrality

  AUTHORS: Karl H. Schlag, Joël J. van der Weele

  KEYWORDS: Belief Elicitation; Proper Scoring Rules; Lottery Tickets; Risk Preferences

  JOURNAL NAME: Theoretical Economics Letters, Vol.3 No.1, February 26, 2013

  ABSTRACT: We are interested in incentivizing experimental subjects to report their beliefs truthfully, without imposing assumptions on their risk preferences. We prove that if subjects are not risk neutral, it is not possible to elicit subjective probabilities or the mean of a subjective probability distribution truthfully using deterministic payments schemes, which are predominant in the literature. We present a simple randomization trick that transforms deterministic rewards into randomized rewards, such that agents with arbitrary risk preferences report as if they were risk neutral. Using this trick, we show how to elicit probabilities, means, medians, variances and covariances of the underlying distribution without assuming risk neutrality.