The costs and benefits of expanding incarceration beyond current levels are now considered. This is a particularly relevant policy question at a time when there seems to be broad consensus among policy makers and the public in favor of controlling rising crime rates through increased use of incarceration, but when there are serious resource constraints on available prison capacity.

To achieve higher levels of incapacitation, policy makers may increase either Q or S. For example, one option would increase the fraction of convictees who are sentenced to prison, thereby raising Q. Alternatively, the fraction of convictees committed to prison might remain constant, but those going to prison would be sentenced to longer terms, which would increase S. Of course, mixed strategies that simultaneously increase both Q and S are also possible, and the policy choice is then to specify the desired balance between broadening the offender base that goes to prison and lengthening prison terms.

Assessing incapacitation effects by analyzing the criminal histories of a sample of convictees in the Denver area, Petersilia and Greenwood (1978) found some evidence to suggest that a policy of short sentences applied to a large offender base is more efficient than a policy of long sentences applied to a small offender base. For example, they estimated that if all convictees in their sample had been given prison terms of one year, regardless of their prior criminal records, the crimes generated by the cohort would have been reduced by 15 percent at a cost of a 50 percent increase in prison population. In contrast, they found that mandatory minimum prison terms of four years imposed only on convictees who had a prior felony conviction would have resulted in the same reduction in crime, but at a cost of a 150 percent increase in the size of the prison population.

From the perspective of the separate contributions of λ and career termination to total offending, the findings of Petersilia and Greenwood are to be expected. The differential impact of Q and S on incapacitation derives fundamentally from career termination. The value of Q is critical in determining how early in an offender's criminal career incapacitation begins to operate. When Q is very small, offenders can be expected to commit numerous crimes before they are caught and incapacitated, and some offenders may survive their entire careers without a single criminal justice system intervention. As Q increases, the number of crimes before an offender's first conviction declines, so a larger Q results

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