# Courts as interpreters of evidence: The economics of updating of information

Legal rules and the decisions taken by courts can influence market outcomes by creating 'price' signals and altering individual incentives. One minimalist way of viewing courts (or judges or juries) is simply as arbiters who process information and in doing so provide information to others in the economy.

To understand this "information processing" role and some of its consequences, consider the following simple example. Denote by *G* the event that an individual has committed a criminal act, and *I* the event that the individual has not. The judge (or jury) does not know for sure whether the individual is guilty or not, but the parties to the dispute each know whether the individual is guilty. The judge (or jury) has no preferences over the outcome itself, although they may incur costs if the decision turns out to be wrong.

Suppose that in the absence of evidence, the court's unconditional probability or *prior belief* of guilt is p(G). The presentation of *evidence *before a court conveys information about guilt or innocence. Suppose that there is a piece of evidence *E* which is suggestive of guilt, but is not conclusive. The event of no evidence arising is denoted by *NE.* The probability of observing evidence and that the defendant is guilty is *P **p(G* ПE. The probability that the evidence arises if the individual has committed the act is:

On the other hand, the probability that the evidence arises if the individual has *not* committed the act is

The probability that evidence will actually emerge is therefore:

The court updates its prior beliefs by computing the probability of guilt, conditional on evidence of guilt having been presented, through the use of Bayes' rule. This probability is denoted by *p(G* | E), and is equal to: