themselves influenced by prevailing sanction levels. In particular, the rate at which offenders have been observed to commit crimes while they are free, λ0 (e.g., in offender self-reports), is influenced by the sanction risks, Q0S0, that those offenders faced while they were free. If sanctions were to change markedly from prevailing levels, it would be reasonable to expect corresponding changes in offending rates while free and thus changes in the base level of potential crimes from which incapacitation is measured.

Although changes in λ constitute a genuine cause for concern, existing estimates of incapacitation are not completely without value. In acknowledging the potential role of sanctions in determining the base level of crimes, incapacitation is measured not against a standard of crimes when incarceration is totally absent, but rather against the level of crimes that would be expected if, despite the prevailing level of sanction risks, offenders were to remain free. The base offending level, λ0, is the rate at which an offender commits crimes conditional upon the prevailing risk of incarceration Q0S0. In an expected utility formulation, λ0 might be regarded as the rate of offending at which the expected benefits from crime equal the expected costs from incarceration for those crimes.

The estimates of incapacitation discussed in this paper should be interpreted in this way. So, for example, the 41.3 percent reduction in crime in Michigan (Table 9) is not the reduction from the expected level of crime if Q0S0 were reduced from 0.0514 (Table 6) to zero in Michigan. Rather, it is the reduction from the level of crime that would be expected if offenders were fortunate and avoided incarceration despite a prevailing expected time served per robbery of 0.0514 year. Such conditional estimates are useful for gauging the relative magnitude of crime reduction from incapacitation in static comparisons across jurisdictions with different prevailing values of λ0 and sanction policies, Q0S0, and for assessing the likely impact of short-term marginal changes from Q0S0. They are less well suited, however, for analyzing the impacts of substantial long-term shifts in policy, such as those observed in recent decades in the United States.

Deterrence effects that alter the size of the active offending population, the offending rates of active offenders, or the duration of offending careers will have important implications for the magnitude of crime reduction that derives from incapacitation. Because they affect the potential crime levels against which incapacitation effects are measured, decreases in the general level of offending also reduce the incapacitative effect. Although deterrence

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