light of an average time served (QS) of less than one month per robbery committed in the three states examined.42

The relationship between the composition of the offender population and incapacitation is also well illustrated by the variation in I* across states. Texas has the highest sanction level (QS = 0.0776), but the lowest incapacitation effect. Two factors contribute to this seemingly paradoxical outcome. First, the mean λ for robbery in the total offender population in Texas is less than half of that in California or Michigan (see Table 8). Second, even high-λ robbers in Texas commit crimes at lower rates than their counterpart high-λ offenders in either California or Michigan, and they comprise a smaller proportion of the total offender population (see Table 7). It is thus not surprising that more crimes are prevented for each robber incarcerated in California than in Texas. The incapacitation index measures the fraction of potential crimes that are averted through incarceration, and as shown by Cohen (1978), the less potential crime in a community, the smaller are the returns from incapacitation.

Remaining Sources of Bias in Incapacitation Estimates

Some important potential sources of measurement bias remain in the estimates of incapacitation reported so far. We discuss these factors briefly below and indicate the direction of the biases they may introduce. Unfortunately, the models and data currently available do not permit rigorous treatment of these biases. Nevertheless, existing knowledge provides some basis for speculating on whether or not these biases are likely to be sizable.

Relationship Between λ and Q. The estimates of incapacitation—both average and marginal—assume a risk of incarceration for each crime committed, Q, that is homogeneous across all offenders. Thus, the crimes of high- and low-λ offenders alike are assumed to be equally vulnerable to interception by the criminal justice system. Heterogeneity in λ coupled with homogeneity in Q leads to overrepresentation of high-rate offenders among prison inmates, which increases the incapacitation index considerably.43

If λ and Q were inversely related—so that high-rate offenders were more likely to escape imprisonment following commission of a crime—the selection effect toward high-λ offenders into prison would be attenuated or could even be reversed, with obvious negative consequences for incapacitation. Consider one extreme in which the most active offenders are completely invulnerable to arrest,

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