A Model of Optimal Incapacitation

Abstract

One of the functions of the criminal sanctions of imprisonment and the death sentence is to prevent individuals from doing harm by removing them from the population.' This incapacitative function of sanctions is considered below in a model in which the amount of harm individuals cause each period that they are free is not influenced by the threat of sanctions (so as to abstract from the role of sanctions as a deterrent).2 The model is initially examined assuming that an individual's dangerousness (i.e., the harm he will do if free) remains the same each period of his life, and that the sanction is imprisonment. In this case, it is optimal to imprison an individual if his dangerousness exceeds a threshold equal to the per period social cost of imprisonment. Moreover, if it is optimal to imprison an individual at all, it will be best to do so for life. The optimal probability of apprehension is also determined. The model is then extended in several ways. It is first supposed that the dangerousness of individuals declines with age. In this case, it is again optimal to imprison individuals if their dangerousness exceeds the per period cost of imprisonment, but it is optimal to release them if their dangerousness later falls below the threshold. It is next supposed that the dangerousness of individuals declines with time spent in prison due to a rehabilitative effect. In this case, it is optimal to imprison individuals beginning at a lower threshold of dangerousness than the per period cost of imprisonment (imprisonment is now socially more valuable) and to release them if their dangerousness becomes sufficiently low. Finally, it is supposed that a choice can be made between imprisonment and the death penalty, and the optimal choice is discussed.

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