Scaling behaviour in the number of criminal acts committed by individuals

We examine the distribution of the extent of criminal activity by individuals in two widely cited data bases. The Cambridge Study in Delinquent Development records criminal convictions amongst a group of working class youths in the UK over a 14 year period. The Pittsburgh Youth Study measures self-reported criminal acts over intervals of six months or a year in three groups of boys in the public school system in Pittsburgh, PA. The range of the data is very substantially different between these two measures of criminal activity, one of which is convictions and the other self-reported acts. However, there are many similarities between the characteristics of the data sets. A power law relationship between the frequency and rank of the number of criminal acts describes the data well in both cases, and fits the data better than an exponential relationship. Power law distributions of macroscopic observables are ubiquitous in both the natural and social sciences. They are indicative of correlated, cooperative phenomena between groups of interacting agents at the microscopic level. However, there is evidence of a bimodal distribution, again in each case. Excluding the frequency with which zero crimes are committed or reported reduces the absolute size of the estimated exponent in the power law relationship. The exponent is virtually identical in both cases. A better fit is obtained for the tail of the distribution. In other words, there appears to be a subtle deviation from straightforward power law behaviour. The description of the data when the number of boys committing or reporting zero crimes are excluded is different from that when they are included. The crucial step in the criminal progress of an individual appears to be committing the first act. Once this happens, the number of criminal acts committed by an individual can take place on all scales.