# The effects of legal errors

The previous analysis assumed that if an individual did not commit an illegal act, they would not be liable for punishment. But courts and juries are not perfect, and sometimes make incorrect decisions.

Let us consider a criminal justice system which operates with errors. Specifically, consider the following kinds of errors:

- • Type I error: a person who does not commit a crime is found guilty.
- • Type II error: a person who does commit a crime is found not guilty.

Let e_{1} be the probability of a type I error, and let e_{2} be the probability of a type II error. We continue to assume that individuals are risk-neutral. For simplicity, we assume that the individual now has two choices with respect to criminal activity: he can either commit a crime (from which he receives a benefit B), or he can choose not to commit a crime, in which case he receives nothing. If the probability of detection and the fine are fixed at *p* and f what is the effect of type I and type II errors on the incentive to commit crime?

If an individual commits a crime, let us assume that he is still arrested with probability *p*, but now there is a possibility that he will not be fined. This means that his expected benefit from committing crime is:

Notice that if *e _{2} =* 0 (that is, no type II errors occur), then this collapses to

*B - pf*, which is the discrete version of the expression that we derived earlier in equation (9.2). On the other hand, if the individual does not commit any crime, the expected benefit is:

Notice that if *e _{1}*

*=*0 (that is, no type I errors occur), then this collapses to 0. Thus, expected net benefits the net gain from committing a crime is:

This is increasing in both e_{1} and e_{2}. In other words, *both types of errors create a greater incentive for risk-neutral individuals to commit crime. *Intuitively, on the one hand, a higher *e _{2}* means that individuals who would have committed crime in any case now have a greater incentive to do so, since there is a possibility that they will be found not guilty when they in fact committed the crime. On the other hand, a higher

*e*means that individuals who might

_{1 }*not*have committed crime now have an incentive to do so, since there is a possibility that they will be found not guilty even when they in fact do not commit crime.