A Mathematical Analysis of Domestic Terrorist Activity in the Years of Lead in Italy

The data-set of the casualties of terrorist attacks in the Years of Lead in Italy is analyzed in order to empirically test theoretical open issues about terrorist activity. The first is whether Richardson’s law holds true when the scale is narrowed down from global to only one epoch of domestic terrorism in a single country. It is found that the power law is a plausible model. Then, the distribution of the inter-arrival times between two consecutive strikes is investigated, finding (weaker) indications that also for this parameter a power law is a plausible model and that this is the result of non-stationary dynamics of terrorist activity. The implications of this finding on the models available today for explaining a power law in the severity of attacks are then discussed. The paper also highlights the counter-intuitive implications that a power law distribution of the waiting times has for a State inferring the time to the next strike from the observation of the time already elapsed since the previous one. Further, it is shown how the analysis of the inter-arrival times provides estimates about the temporal evolution of terrorist strength that can help discriminating among competing hypotheses derived from qualitative analysis. Finally, a simplified mathematical model of the policy decision-making process is constructed to show how the nature of power laws biases the prioritizing of the policy agenda and the consequent allocation of resources to concurring issues. It is shown how the bias causes systematical relative underfunding of policy issues whose severity follows a power law distribution and that this trend is likely to persist until a major event will reverse the behavior of the decision-maker, then causing relative overfunding.