On the statistical properties and tail risk of violent conflicts

Abstract

We examine statistical pictures of violent conflicts over the last 2000 years, finding techniques for dealing with incompleteness and unreliability of historical data. We introduce a novel approach to apply extreme value theory to fat-tailed variables that have a remote, but nonetheless finite upper bound, by defining a corresponding unbounded dual distribution (given that potential war casualties are bounded by the world population). We apply methods from extreme value theory on the dual distribution and derive its tail properties. The dual method allows us to calculate the real mean of war casualties, which proves to be considerably larger than the sample mean, meaning severe underestimation of the tail risks of conflicts from naive observation. We analyze the robustness of our results to errors in historical reports, taking into account the unreliability of accounts by historians and absence of critical data. We study inter-arrival times between tail events and find that no particular trend can be asserted. All the statistical pictures obtained are at variance with the prevailing claims about "long peace", namely that violence has been declining over time

The Decline of Violent Conflicts: What Do the Data Really Say?

“…The dual distribution approach, based on a special log-transformation of data, is the way in which we deal with apparently infinite mean phenomena like war casualties. For more details about our methodology, especially for the use of the dual distribution, we refer to Cirillo and Taleb (2016).…”

“…We also establish that violence has a "true mean" that is underestimated in the track record. This is a historiographical adaptation of the results in Cirillo and Taleb (2016). …”

“…Our paper Cirillo and Taleb (2016) set to construct the most statistically robust picture of historical violence for "named conflicts" we could make under the constraints given by these five problems. To deal with the first problem (Fat tails) we made use of a branch called Extreme Value Theory.…”

“…Figure 6 is a Zipf plot (mentioned earlier), and it represents a heuristic tool to look for Paretianity in data (Cirillo, 2013), by using a property of the survival function of a Pareto distributed random variable. Many other plots can be used to verify the presence of a fat right tail, such as Maximum-to-Sum and mean excess plots, and we refer to Cirillo and Taleb (2016) for more details and discussions. The linearity of the survival function starts indeed from the very left-hand side of the plot.…”

The Evolution of Civil War Severity, 1816–2005

“…Among the many features that may affect conflict severity, population size is likely to exert a particularly strong impact on the magnitude of a conflict, and the severity of a conflict relative to population is also an important aspect of a conflict's relative impact (see Cirillo and Taleb 2015;Pinker 2011). Accordingly, we propose the relative number of casualties, or the number of casualties per hundred thousand inhabitants, as a measure of conflict impact.…”