Analysis of the decision rule in Epstein´s Agent-Based model of civil violence

In this work we present an analysis of the theoretical foundations and underlying mechanisms modelled by the decision rule in Epstein´s Agent-Based model of civil violence and the associated arrest probability function, by considering related areas of research, such as ethology, predator-prey systems, detection theory and threshold models of binary decision with external influences. We determined the conditions for the occurrence of cascades and large bursts of rebellion in terms of the analytical form of the probability distributions of grievance and net risk perception for two different arrest probability functions using Mathematica, and confirmed their validity via an Agent-Based model implemented in NetLogo. It was shown that cascades and large rebellion peaks occur if the arrest probability function leads to a mechanism of `massive threshold lowering´ of the risk perception when the deterrence level falls below a critical value. We also derived general conditions for the stability of the solutions and discussed their practical implications.