Nonlinear Utility and the Probability Score

Proper scoring rules, such as the probability score, are based (in part) upon the assumption that the assessor's utility function is linearly related to the score. The effects of two nonlinear utility functions, one representing a “risk-taker” and one representing a “risk-avoider,” on an assessor's probability forecasts are considered. The results indicate that factors other than the expected score, e.g., the variance of the score, may be relevant for probability assessment. In general, a “risk-taker” “hedges” toward a categorical forecast, while a “risk-avoider” “hedges” away from a categorical forecast. The implications of these results for the process of probability assessment are briefly discussed.