Limits for the Precision and Value of Information from Dependent Sources

In many inferential and decision-making situations, information is obtained from a number of information sources, and the separate pieces of information are often not independent. This paper investigates the impact of dependence on the precision and value of information. The results indicate that positive dependence among information sources can have a serious detrimental effect on the precision and value of the information. Differences in precision between the dependent and independent cases can be remarkably large. With dependence, the incremental value of information can decrease very rapidly, and the limiting value of information as more sources are considered can be considerably less than the expected value of perfect information. The results of this paper have implications for the acquisition and use of information in decision-making problems.