Simple mathematical law benchmarks human confrontations

Abstract

Many high-profile societal problems involve an individual or group repeatedly attacking another – from child-parent disputes, sexual violence against women, civil unrest, violent conflicts and acts of terror, to current cyber-attacks on national infrastructure and ultrafast cyber-trades attacking stockholders. There is an urgent need to quantify the likely severity and timing of such future acts, shed light on likely perpetrators, and identify intervention strategies. Here we present a combined analysis of multiple datasets across all these domains which account for >100,000 events, and show that a simple mathematical law can benchmark them all. We derive this benchmark and interpret it, using a minimal mechanistic model grounded by state-of-the-art fieldwork. Our findings provide quantitative predictions concerning future attacks; a tool to help detect common perpetrators and abnormal behaviors; insight into the trajectory of a ‘lone wolf'; identification of a critical threshold for spreading a message or idea among perpetrators; an intervention strategy to erode the most lethal clusters; and more broadly, a quantitative starting point for cross-disciplinary theorizing about human aggression at the individual and group level, in both real and online worlds.

Spatio-temporal patterns of IED usage by the Provisional Irish Republican Army

“…Specifically for the case of NI this paper is focused on the group known as the Provisional Irish Republican Army (PIRA). Although there are extensive historical accounts and a growing body of social science research related to this group [3,19,25,26,51] there is a gap for a wider scope of mathematical investigations of their activities.…”

Formation of raiding parties for intergroup violence is mediated by social network structure

“…Evolutionary models have credited collective violence with an important role in the development of modern human behavior (2-7), whereas cultural and ecological factors have been shown to influence small and largescale violence (8)(9)(10)(11)(12)(13). More recently, there has been increased interest in understanding the dynamics of group-based violence and the social processes that can contribute to it in the setting of insurgent and terrorist groups (14,15); for example, online records suggests small, self-organizing groups coalesce into larger groups preceding terrorist attacks (16). Warfare has also been studied as a collective action problem-because individuals must mobilize to engage in a group activity with shared gains (e.g., deterrence, territory) and individual risks (e.g., injury, death) (17,18).…”

Modeling Human Conflict and Terrorism Across Geographic Scales

“…This follows from the well-known central limit theorem. In the special case that steps in R.n/ have the same size, this [49] result is equivalent to the statement from elementary statistics that the variance of the sum of uncorrelated variables is equal to the sum of the variances.It is known from statistical physics that for more general stochastic walks with implicit correlations between changes in R.n/, Red's advantage (and hence the rate of Red attacks) will still vary as jR.n/j rms nˇbut withˇ¤ 0:5. Hence the time between attacks will vary as jR.n/j 1 rms n ˇ.…”

“…Indeed, the fact that more detailed spatiotemporal data is now becoming available, often down to the daily scale within individual provinces or districts, means that the bar has been raised in terms of what a model needs to achieve in order to be considered consistent with the data. Our data sources are a mix of real-time media databases, official (government and non-governmental organization) reports, and academic studies [49]. Some of our data was obtained from Uppsala Conflict Data Program.…”