A Spinglass Model of Video Recorded Street Violence

When groups encounter challenges in uncertain situations, collective action—in our case attack of or defense against opponents—has been explained by models of thresholds, cascades, and critical mass. These models draw on initiative takers or leaders to initiate cooperation. We use an Ising spinglass model with asymmetric spin values, which is more parsimonious because it has no assumptions on initiative takers or leaders. It shows that cooperation can start by accidental cooperators rather than exceptionally zealous ones. More importantly, our model makes a novel prediction about the temporal unfolding of collective action. When a proportion of group members, p, does not cooperate, versus 1 - p conditional cooperators who may cooperate if enough others do, a mean field analysis predicts that collective action breaks out in a burst if p is below a critical value. Above the critical value there is no burst but a fizzle of one individual or few group members who start cooperating asynchronously. Furthermore, small groups and small clusters in large groups are more easily agitated to cooperate than large groups. The predicted critical value, the two temporal patterns, and the size effect are strongly supported by video data of street fights between a focal group against one or more opponents.