Bayesian consistent belief selection

A subjective expected utility agent is given information about the state of the world in the form of a set of possible priors. She is assumed to form her beliefs given this information. A set of priors may be updated according to Bayes’rule, prior-by-prior, upon learning that some state of the world has not obtained. In a model in which information is completely summarized by this set of priors, we show that there exists no decision maker who obeys Bayes’rule, conditions her prior only on the available 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. yDepartment of Economics, University of Texas at Austin, BRB 1.116, Austin, TX 78712. Email: [email protected]. Phone: (512) 475-8543. zCorresponding author. xWe would like to thank Kim Border, Federico Echenique, Larry Epstein, Bart Lipman, Max Stinchcombe, John Quiggin, and Bill Zame for helpful discussions and comments. The associate editor and two anonymous referees also provided comments which were very helpful. All errors are our own.