Since utilities and probabilities jointly determine choices, event-dependent utilities complicate the elicitation of subjective event probabilities. However, for the usual purpose of obtaining the information embodied in agent beliefs, it is su#cient to elicit objective probabilities, i.e., probabilities obtained by updating a known common prior with that agent's further information. Bayesians who play a Nash equilibrium of a certain insurance game before they obtain relevant information will afterward act regarding lottery ticket payments as if they had event-independent risk-neutral utility and a known common prior. Proper scoring rules paid in lottery tickets can then elicit objective probabilities.

Proper scoring rules (PSR) are among the most popular incentivized belief elicitation mechanisms. A well known result is that risk averters facing PSR misreport their beliefs by stating more uniform probabilities. We show that this result does not generalize when i) the PSR payments are increased, ii) the agent has a …nancial stake in the event she is predicting, and iii) the agent can hedge her prediction by taking an additional action. Instead, combining theory and experiment, we …nd that agents distort their reported probabilities in complex, yet mostly predictable manners. We argue that our results have implications for the elicitation of beliefs in most environments of interest to economists, both in academia and in practice. We would especially like to thank Amadou Boly and Alexander Wagner for their help and insights during the course of this research project. We also thank seminar participants at Bergen and the 2009 ESA conference in Tucson for helpful discussions. All remaining errors are ours. The views expressed in this paper are those of the authors and do not necessarily represent the views of the Federal Reserve Bank of New York, or the Federal Reserve System.