Abstract
We examine the subjective value of gaining knowledge in a version of Savage's model for decisions under uncertainty in which the received outcome provides information about which event has obtained. Decision makers commonly value such knowledge either because they want to use it in future decisions or because they are personally interested in it. We find that in our model, the sure-thing principle and several other axioms of Savage are inconsistent with this value for knowledge about events. We provide a representation theorem for a subjective value of knowledge consisting of the sum of expected utility and a function of the information partition generated by the outcomes of an act. We characterize when the value of knowledge can be represented by a subjective value of knowledge about an information partition plus a Shannon entropy cost of processing information. Our results also provide a novel critique of the necessity of Savage's axioms for rational decisions under uncertainty.
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