Individual error, group error, and the value of information

This paper studies the interaction of error and information both in a single-person setting and in an interactive setting. In contrast to Blackwell's Theorem, which says that more information is always good, the perspective of this paper is that while a lot of information is beneficial, a little information can be harmful. The main achievements of this paper are: (1) A characterization of the class of signals which always benefit a decision-maker in all decision problems. The analysis is carried out in a model which allows for the possibility that the decision-maker makes a mistake. (2) A demonstration that there are public signals within this class which can nevertheless reduce the utility of a team (i.e., a collection of agents wit a common objective), as well as a characterization of the clas of signals which always benefit a team in every team game. (3) A theorem that shows that in decision problems, beyond a certain threshold of precision, the value of information is increasing in the precision of signals, and which also provides a characterization of this threshold.