Abstract

What if residents of a neighbourhood could influence crime rates through their behaviour? This is what postulates the theory of collective efficacy. Collective efficacy is the conviction shared by a group of people that they can work together to successfully complete a specific task. The idea is that the difference in neighbourhoods’ inner structure leads to spatial variation in crime rates. Many models exist that show the negative link between collective efficacy and crime but the literature in studying the formation of patterns is still limited. We present a novel convolution model of collective efficacy that allows for a mathematical investigation of neighbourhood and resource effects on the formation of collective efficacy and transitions between different regions of collective efficacy.