Preference for Flexibility and Bayesian Updating

Dekel, Lipman, and Rustichini (2001) show that preferences over menus of lotteries can be represented by the use of a unique subjective state space and a prior. We provide foundations for Bayesian updating in such a setup. When the subjective state space is finite, we show that Bayesian updating is linked to a comparative theory of preference for flexibility. Without the finiteness of the subjective state space, Bayesian updating is characterized by a more technical condition.