[Paper Review] On the tail risk of violent conflict and its underestimation

Pasquale Cirillo, Nassim Nicholas Taleb|arXiv (Cornell University)|May 18, 2015

Financial Risk and Volatility Modeling5 citations

TL;DR

The paper proposes a novel extreme value theory approach using a dual unbounded distribution to model fat-tailed, finite-bound war casualty data, revealing that the true mean of war casualties is substantially higher than the sample mean due to underestimation of tail risks; this challenges the widely held belief in a long-term decline in violence.

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.

Motivation & Objective

• To address the statistical challenges posed by incomplete and unreliable historical data on violent conflicts over the past 2000 years.
• To develop a method for accurately estimating tail risks of violent conflict despite finite upper bounds on casualties (e.g., world population).
• To correct the systematic underestimation of extreme war casualties caused by reliance on sample means from sparse historical records.
• To test the robustness of tail risk estimates against errors and omissions in historical reporting.
• To reassess the claim of a long peace by analyzing inter-arrival times and tail event trends in conflict data.

Proposed method

• The authors define a dual unbounded distribution corresponding to the true, bounded distribution of war casualties, enabling application of standard extreme value theory techniques.
• They apply extreme value theory to the dual distribution to derive accurate tail properties, including the true mean of casualties.
• The method accounts for the finite upper bound of casualties (world population) by transforming the bounded variable into an unbounded dual form.
• Statistical robustness is tested by simulating errors and omissions in historical reports to assess sensitivity of tail risk estimates.
• Inter-arrival times between extreme conflict events are analyzed to detect temporal trends in tail event frequency.
• The approach allows for inference on the true severity of conflict tail risks even when historical data is sparse or biased.

Experimental results

Research questions

• RQ1 To what extent are extreme war casualties systematically underestimated when relying on sample means from incomplete historical data?
• RQ2 How can extreme value theory be adapted to fat-tailed, bounded variables such as war casualties?
• RQ3 What is the true mean of war casualties when accounting for the finite upper bound imposed by world population?
• RQ4 Are there detectable trends in the inter-arrival times of extreme conflict events over the past 2000 years?
• RQ5 Does the statistical picture of conflict severity contradict the prevailing narrative of a long peace?

Key findings

• The true mean of war casualties is substantially higher than the sample mean, indicating severe underestimation of tail risks.
• The dual distribution method successfully enables extreme value analysis on bounded fat-tailed variables by transforming them into unbounded equivalents.
• The method demonstrates robustness to errors and omissions in historical reports, validating its reliability under data uncertainty.
• No significant trend is found in the inter-arrival times between extreme conflict events, suggesting no consistent increase or decrease in tail event frequency.
• The statistical analysis contradicts the claim of a long peace, as the data shows persistent and substantial tail risks of violent conflict.
• The results imply that the risk of catastrophic conflict remains far greater than commonly assumed in historical and policy discussions.