Weak Informativeness: An Information Order with Variable Prior

What can be learned from a signal about the unknown state of the world not only depends on the precision of the signal technology, but also on the degree and nature of the prior uncertainty. Therefore, a general information... [ view full abstract ]

What can be learned from a signal about the unknown state of the world not only depends on the precision of the signal technology, but also on the degree and nature of the prior uncertainty. Therefore, a general information system is a tuple consisting of both a technology and a prior. In this paper we define an information order for general information systems and characterize the order in two different ways: first, in terms of the dispersion of posterior beliefs and, second, in terms of the value of information for a class of agents with quasi-linear preferences. We then apply our findings to a particular investment problem and show that informativeness is increasing in leverage. Hence, the same technology is more valuable for a leveraged than for a non-leveraged investor.