Proper scoring rules for general decision models

On the domain of Choquet expected utility preferences with risk neutral lottery evaluation and totally monotone capacities, we demonstrate that proper scoring rules do not exist. This implies the non-existence of proper scoring rules for any larger class of preferences (CEU with convex capacities, multiple priors). We also show that if a decision maker whose behavior conforms to the multiple priors model is faced with a scoring rule for a subjective expected utility decision maker, she will always announce a probability belonging to her set of priors; moreover, for any prior in the set, there exists such a scoring rule inducing the agent to announce that prior. Keywords: scoring rule, subjective expected utility, implementation, multiple priors, Choquet expected utility, probability elicitation. JEL classi…cation: D81, C49 Assistant Professor of Economics, Division of the Humanities and Social Sciences, Mail Code 228-77, California Institute of Technology, Pasadena, CA 91125. Email: [email protected]. Phone: (626) 395-3559. I would like to thank Federico Echenique, PJ Healy, and John Ledyard for comments and suggestions.