In my recent talk on Alfred Blumstein’s *Crime modeling*, I briefly discussed how optimization has been used in crime modeling. The consensus was that the problems were simply too complex to model effectively. Consider the usual process for incarceration, which involves countless different entities. An arrest is made. Court appearances are had. Bails are set. Plea bargains are discussed. A trial takes place. A sentencing decision is made. Each case is a unique, gavel-shaped snowflake.

Regardless, efforts have been made to optimize certain aspects of “crime modeling.” One of these is a 2001 paper by Gernot Tragler, Jonathan Caulkins, and Gustav Feichtinger. It attempts to allocate the use of treatment and enforcement resources to mitigate the use of drug trafficking. The problem is tackled from a control theory perspective. The authors note that neither treatment or enforcement is unilaterally superior to the other in combating drug proliferation. Any viable drug control model will result in a solution that varies the use of treatment and enforcement as time progresses.

Tragler’s paper suggests two policies for dealing with new drug problems. The first is “eradication”, a policy that attempts to completely remove the new drug problem before it spirals out of control. This policy is only advisable when the problem is indeed fast-spreading, it is detected early, and policymakers are able to devote large amounts of resources to wipe out the problem. The last of these is a political conundrum; successfully eradicating a potential drug epidemic does not necessarily positively change public perception of a policymaker, because the problem was never allowed to reach a critical level. In fact, funneling financial resources to combat a problem that never becomes overly serious could have an *adverse* effect on the policymaker’s career. The eradication policy directs enormous amounts of enforcement and treatment to fight the drug problem right away. However, if any of the three aforementioned conditions are not satisfied, it is advisable to pursue a less drastic policy. “Accommodation” begins with a large amount of enforcement. Enforcement grows as the drug problem grows, though not at as fast of a rate. Treatment resources, on the other hand, grow proportionally with the proliferation of the drug problem.

An earlier effort at incorporating optimization and crime modeling was made by Blumstein and Daniel Nagin. The two attempt to determine the *proportion* of convicted offenders who become imprisoned and the *average time* to be served by these imprisoned offenders. The goal is to minimize the total crime rate. The obvious solution to minimize the total crime rate is to incarcerate as many offenders as possible for as long as possible. Naturally, this will not work; the authors impose the constraint that the total amount of imprisonment cannot exceed a certain amount. This constraint makes sense in our real world, where overpopulation in prisons is a glaring issue.

Quite possibly the most important result of this work was its admission that simply more work had to be done. The parameters used in the model needed more data to accurately estimate. Furthermore, the model could be modified and expanded to account for multiple crime rates. However, as Blumstein would note 24 years later, the world of crime modeling is often too complex for optimization models.

Blumstein, A. (2002). Crime modeling. *Operations Research*, 50(1), 16-24.

Blumstein, A., & Nagin, D. (1978). On the optimum use of incarceration for crime control. *Operations Research*, 26(3), 381-405.

Caulkins, J.P., Feichtinger, G., & Tragler, G. (2001). Optimal dynamic allocation of treatment and enforcement in illicit drug control. *Operations Research*, 49(3), 352-362.

Good post! I think we have learned a lot since many of the harsh sentences from the 1990s. I’d love to see judges consider math modeling when they are sentencing people, but that seems capricious in terms of our values as a society. We have the view that the punishment should fit the crime and the individual and maybe not reflect other at a societal level. Some of Blumstein’s early work noted that prison populations were more or less kept at steady state–more prisoners were paroled when the prison population got too high as to avoid costly increases associated with building more prisons–but that was not an official policy. Judges did not announce in court that “This algorithm told me it’s time to parole you.” I doubt that we’ll get there, but hopefully math can give some insight to how to fight crime while not letting costs spiral out of control.

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