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.

我们研究了在萨维奇模型的一个版本中获取知识的主观价值，以在不确定的情况下进行决策，其中收到的结果提供了有关已获得哪个事件的信息。决策者通常重视这些知识，要么是因为他们想在未来的决策中使用它，要么是因为他们个人对此感兴趣。我们发现，在我们的模型中，萨维奇的确定性原则和其他几个公理与事件知识的这种价值不一致。我们提供了知识的主观价值的表示定理，该知识的主观价值由预期效用之和以及行为结果生成的信息划分的函数组成。我们描述知识的价值何时可以由有关信息分区的知识的主观价值加上处理信息的香农熵成本来表示。我们的结果还对萨维奇公理对于不确定性下理性决策的必要性提出了新颖的批判。