A Note on Optimal Sentencing with Recurring Crime and Adjudication Errors

We analyze optimal sentence length for recurring crimes in the face of adjudication errors. We develop an infinite-horizon model where offenders are habitual---they repeat crimes whenever free. If apprehended, criminals may be wrongfully acquitted. Similarly, innocent persons may be apprehended and wrongfully convicted. The key finding is that, under reasonable conditions, the two types of adjudication errors have opposite effects on optimum sentencing. Sentence length should decrease with the risk of wrongful convictions, and increase with the risk of wrongful acquittals.