Proper Scoring Rules and Risk Aversion

The literature on proper scoring rules has mostly studied the case of risk neutral agents. We analytically investigate how risk averse, expected utility maximizing forecasters behave when presented with risk neutral proper scoring rules. If the state variable is binary, risk averse agents shade their reports toward saying that the states are equally likely. In the non-binary case reported probabilities are compressed relative to truthtelling. We show the implications of our results for the use of elicited probabilities as inputs to decision-making and find that naive elicitors may violate first-order stochastic dominance. Possible resolutions of these problems are presented, including an estimator for the mean population belief when the distribution of risk attitudes is known. Finally, we discuss the relevance of our results to recent work in experimental economics.

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