# Policy 3: Release Prisoners

### Description

A one-time release of prisoners could be (and has been) implemented in multiple ways, including releasing:

• a) Those with the least time remaining on their sentences
• b) Those who have committed the least serious crimes
• c) The oldest or most ill inmates

The calculation for each type of release is similar; only the exact parameter values differ. I assume that here a one-time release of $$N$$ prisoners, which results in a mean sentence reduction of $$D$$ days.

The general deterrent effect depends on how potential offenders view the release. If it is truly seen as a one-time release, then it will have no impact on their expectation of future punishment and thus no cost due to decreased general deterrence. If potential criminals do think a prisoner release is likely to be repeated within their offending careers, then it will decrease their expected sentence length and should have a general deterrence cost. The magnitude will depend on their assessment of the likelihood of recurrence and the specific type of release. I assume that potential criminals do not update their expected sentence based on one-time releases and thus that $$Cost_{GD}=0$$.

As discussed in the section on specific deterrence, there have been at least two studies of exactly such prisoner releases. These provide estimates for the cost of such releases by virtue of decreased specific deterrence which can be quantified as: $Cost_{SD}=c_\theta\frac{D}{365}*\frac{drecid}{ds}*\lambda$ where $$c_\theta$$ is the cost per crime that will not be specifically deterred due to the shorter sentence. The parameter $$\theta$$ is used because the correct cost will likely be below the mean and vary depending on whether the prison release is policy a, b, or c. This equation is an upper bound on specific deterrence costs, assuming that all released prisoners have short enough sentences that a somewhat longer sentence would have decreased crime upon release. With this assumption, $$D*\frac{drecid}{ds}$$ will be the change in recidivism rate per released prisoner and $$\lambda\mathit{N}$$ times the quantity will be the total extra crimes.

It is difficult to know precisely what part of the cost distribution is appropriate to use, but for all three scenarios it should certainly be below the mean. We can conservatively use the tenth or twenty-fifth percentile as the average cost per crime.

The incapacitation effect is once again the easiest component to calculate. It is: $Cost_{Inc}=c_\theta\lambda\mathit{N}\frac{D}{365}$ simply the amount of time the released prisoners will now be free and capable of committing crimes. Again, the correct value of $$c_\theta$$ is certainly below the median, and likely very close to zero for the oldest released prisoners.

The benefit from a prisoner release is due to the reduced prison expenditures and value of freedom loss and may be expressed as: $Benefit=(CP+VoF)N\frac{D}{365}$ That is, the aggregate number of years these prisoners will not be incarcerated $$(N\frac{D}{365})$$ times the sum of the annual prison and value of freedom cost. I now use the best empirical estimates of these parameters as identified in Part II to perform the calculations described.

### Parameters

Select a set of values from the dropdowns below to pre-fill the parameters or use custom values. For more about the papers this calculator refers to, please consult the references section.

 $$c_\theta$$, cost per crime that will not be specifically deterred due to the shorter sentence $$D$$, mean sentence reduction in days $$N$$, number of prisoners in one-time release $$\eta_{Inc}$$, incapacitation benefit of 1% increase in sentence length $$\frac{drecid}{ds}$$, marginal reduction in recidivism rate as sentence length $$s$$ increases # of crimes committed/year # of prisoners/year # of jail inmates/year $$CP_{day}$$, cost/prisoner/day $$VoF_{day}$$, value of freedom/prisoner/day $$\lambda$$, # of potential crimes committed/year if released

### Results

 Benefit: Not Calculated Total Cost: Not Calculated General Deterrence: Not Calculated Specific Deterrence: Not Calculated Incapacitation: Not Calculated Net Benefit: Not Calculated Annualized Net Benefit/Release: Not Calculated