How does the probability of wrongful conviction affect the standard of proof?

Summary The paper inquires into the impact of mistakes of identity (ID errors) on the optimal standard of proof. A mistake of identity is defined as an error such that an individual is punished for someone else’s crime. and for the same crime, the criminal is falsely acquitted. Therefore, the decision to engage in a criminal activity generates a negative externality, as the expected number of ID errors increases. Thus, our objective is to understand how public law enforcement can deal with this type of error by means of the standard of proof. Our main results are twofold. First, we show that when ID errors occur, the under-deterrence issue is exacerbated. Second, we find that the optimal standard of proof may be higher or lower than without ID errors, depending on the crime rate at equilibrium and on the impact of the standard of proof on (i) the probability of an acquittal error for each crime committed, (ii) the probability of convicting an innocent person when an acquittal error arises, and (iii) the level of deterrence.