Research Article: Fundamental patterns and predictions of event size distributions in modern wars and terrorist campaigns

Date Published: October 17, 2018

Publisher: Public Library of Science

Author(s): Michael Spagat, Neil F. Johnson, Stijn van Weezel, Kristian Skrede Gleditsch.


It is still unknown whether there is some deep structure to modern wars and terrorist campaigns that could, for example, enable reliable prediction of future patterns of violent events. Recent war research focuses on size distributions of violent events, with size defined by the number of people killed in each event. Event size distributions within previously available datasets, for both armed conflicts and for global terrorism as a whole, exhibit extraordinary regularities that transcend specifics of time and place. These distributions have been well modelled by a narrow range of power laws that are, in turn, supported by some theories of violent group dynamics. We show that the predicted event-size patterns emerge broadly in a mass of new event data covering all conflicts in the world from 1989 to 2016. Moreover, there are similar regularities in the events generated by individual terrorist organizations, 1998—2016. The existence of such robust empirical patterns hints at the predictability of size distributions of violent events in future wars. We pursue this prospect using split-sample techniques that help us to make useful out-of-sample predictions. Power-law-based prediction systems outperform lognormal-based systems. We conclude that there is indeed evidence from the existing data that fundamental patterns do exist, and that these can allow prediction of size distribution of events in modern wars and terrorist campaigns.

Partial Text

Polymath Lewis Fry Richardson showed, in his seminal work, that war sizes follow a fat-tailed distribution which, he suggested, could be well captured by a power law [1, 2]. Later research has updated and confirmed this finding using more rigorous statistical methods [3–5]. It turns out that the Richardson insight for sizes of whole wars extends to event sizes within wars. For this analysis the size of a discrete event, such as a suicide bombing or a battle, is defined by the number of people killed in the event. The distributions of event sizes within nine modern wars are all well approximated by a power law with the estimated power coefficients clustering around 2.5 [6]. The size distribution for global terrorist events, merging together all events perpetrated by all terrorist groups, is also well captured by a power law with a coefficient around 2.5 [7]. This latter finding has practical utility because the identified empirical regularities can be used to predict the probability of a terrorist attack comparable in scale to the 9/11 one [8, 9].

We take our armed-conflict data from the Georeferenced Event Dataset (GED) of the Uppsala Conflict Data Programme [10]. This is the most comprehensive and accurate georeferenced dataset on armed conflict available [16–18] that systematically collects information on the number of people killed in each event. The GED records details that include the location, timing, and severity of conflict events along with information on the warring parties that generate these events. The data collection effort covers conflicts between governments and rebel groups, non-state based conflicts (also known as communal violence), and violence perpetrated by the state or insurgency groups against civilians. We use the most recent version of the dataset available at time of writing (v.17.2) which covers all conflicts across the globe between 1989-2016. The GED coding rules exclude some low-intensity conflicts by imposing a minimum fatality threshold of 25-battle related deaths in a given year. However, this restriction hardly matters for us since it excludes only minor conflicts that may have been excluded anyway due to not having enough events to allow us to reliably fit a power law to the size distribution of their violent events.

We use the “poweRlaw” package in R [21] to fit the model Ms−α to the data for each conflict above an estimated cut-off value smin using maximum likelihood estimation [12, 22] where s denotes the number of fatalities in an event, α is the power-law coefficient and M is a normalisation factor ensuring that the cumulative probability distribution sums to unity. Fig 1 provides examples of power laws fitted to four conflicts, The smin parameter, the lower threshold, is estimated using a Kolmogorov-Smirnov approach, where the distance between the cumulative density function of the data and the fitted model is minimised [21, 22]. To account for parameter uncertainty, the estimates are obtained using a bootstrap procedure with 1,000 iterations. Fig 2 plots the estimated α values for the 273 conflicts in our sample against the p-values of bootstrapped tests of the hypotheses that their data are generated by the fitted power laws for these conflicts; here the null hypothesis is that the power law distribution cannot be ruled out. To be clear, each data point in Fig 2 summarizes a power law fit for one particular conflict such as each one of the conflicts in Fig 1.

We have investigated the size distribution of violent events in modern conflicts and terrorist campaigns, finding that these are generally well approximated by power laws with α coefficients clustered near 2.5. There are some exceptions, though Figs 2 and 3 show that these exceptions also tend to have large uncertainties in the values of their coefficients. It will be interesting in the future to look in detail at what might make these few conflicts and campaigns so different. We exploit these empirical regularities in the conflict data, without ignoring the anomalies, and are able to make good predictions about the relative frequencies of violent events falling within various size classes. Our success at out-of-sample predictions indicates that our approach should work well for predicting the mixtures of event sizes in future armed conflicts. We recommend using an α near 2.5 for making such predictions, with a possible range of 1.6 to 4.0.




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