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A Dynamical Interpretation of the Three-Strikes Law

California's Three Strikes Law has been in effect since 1994. Advocates of this policy claim it acts as a deterrent for violent crime; yet critics allege it acts solely as an incapacitant-a device used to segregate a population of "undesirables" from the total population in an attempt to lower criminal susceptibility. To determine the true relationship between these two intimately connected phenomena, we construct a dynamical model of the Three-Strikes Law within the framework of inner-city communities located in Los Angeles County. We then compare this model to one of Los Angeles County before California implemented the Three-Strike policy-the classical incarceration model. Through qualitative analysis we determine the basic reproductive number, R0, for each of the models. Using numerical simulations, we then determine the net change in the total population of reformed inmates and the total number of incarcerated individuals due to the Three-Strikes Law. We also analyze the impact of population density on crime rates in states that utilize the Three-Strikes Law. Finally, we construct and examine a hypothetical One-Strike model to determine the impact of different strike policies on the reformed, criminal and incarcerated populations. We find that the Three-Strikes policy deters crime better than the classical incarceration policy in densely populated areas like Los Angeles County. In the context of population density, the Three-Strikes Law is a better deterrent in a sparsely populated region than a densely populated region. The optimal policy is found to be one that consists of more than three strikes.

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Susan Seal, Arizona State University
William Z. Rayfield, University of Maryland Baltimore County
Carl Ballard II, Alabama State University
Holden Tran, Northwestern University
Christopher Kribs-Zaleta, University of Texas at Arlington
Edgar Díaz, Arizona State University