Optimal sentencing with recurring crimes 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 people may be apprehended and wrongfully convicted. The key result shows how the risks of wrongful convictions and wrongful acquittals affect optimal sentencing. For reasonable ranges of parameter values, the two types of adjudication errors have the same qualitative effect on optimal sentencing: a greater risk of any of the two adjudication errors leads to a decrease in optimal sentencing.