The Nonlinear Dynamics of Crime Rates - A Sigmoid Crime Rate Model

• In Event: Advances in Statistical Methods

Abstract

The purpose of this presentation is to show how crime rates follow a nonlinear sigmoid normal response curve with changes in propensity or sanctioning. The sigmoid crime rate model presumes that crimes occur at the intersection between the individual and the society. Crimes are individual acts that are perceived by society to be harmful enough to warrant legal sanctions. There are limitless numbers of factors correlated with an individual’s propensity to harm others. Because of limiting processes, the propensity to cause harm is normally distributed in the population. The sanctioning process is cumulative and asymmetric. People who are more likely to harm others are more likely to be sanctioned for their behavior than those less likely to harm others. Therefore, the sanctioning process will select people from the high end of the normal propensity distribution. If propensity is normal, and sanctioning is asymmetric, the crime rate will follow a sigmoid response curve with changes in propensity or sanctioning. The sigmoid crime rate model will have a number of applications, such as work on the age crime curve, incapacitation models, and work on comparative criminology. In particular, the incapacitation model indicates that increases in incarceration levels will produce rapidly diminishing returns.

Author

• Thomas Kenneth Arnold, University of Cincinnati