On the statistical properties and tail risk of violent conflicts (1505.04722v2)

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 paper introduces a novel EVT-based dual-distribution methodology to estimate the tail risks of war casualties.
• It finds that traditional statistical methods significantly underestimate the 'shadow mean' due to heavy-tailed distributions in a dataset of 565 conflicts.
• The study challenges the 'long peace' hypothesis by demonstrating no declining trend in violent conflict occurrence over two millennia.

Analyzing the Tail Risk and Statistical Properties of Violent Conflicts

The paper by Pasquale Cirillo and Nassim Nicholas Taleb offers a rigorous examination of the statistical nature of violent conflicts over the past 2000 years. The research introduces innovative methodologies to address the challenges posed by incomplete historical data and assesses the tail risks associated with such conflicts. This paper is particularly relevant given the extensive debate among scholars concerning trends in global violence and the hypothesis of a "long peace."

Methodological Insights

A novel contribution of this paper is the adaptation of extreme value theory (EVT) to tackle the complexities associated with fat-tailed variables in bounded distributions, inspired by the philosophical challenge that potential war casualties have an unequivocal upper bound—the world's population. This approach employs a unique transformation to define an unbounded dual distribution, facilitating the application of EVT to derive the tail properties of these conflict-related variables.

The application of EVT to the dual distribution provides an estimation of the "shadow mean" of war casualties, which emerges significantly larger than the sample mean derived from historical observations. This discrepancy underscores the severe underestimation of tail risk when relying on conventional statistical techniques and highlights the importance of rigorous analysis in understanding extreme events.

Key Findings

The research systematically invalidates the claim of a declining trend in violence over time, as espoused by some scholars advocating the "long peace" hypothesis. Through detailed analysis of a dataset encompassing 565 conflicts exceeding 3000 casualties, the researchers find that the distribution of war casualties exhibits a heavy right tail. The emerging evidence problematizes the notion of a statistically significant decline in warfare intensity.

Statistical Observations:

• The mean excess function plots and Pickands estimators suggest a prominent heavy-tailed nature in war casualties.
• An estimated shape parameter $\xi$ significantly greater than 1 implies an infinite expectation for the distribution of casualties within the sample, further confirming the extensive tail risks involved.
• The analysis of inter-arrival times between large conflicts reveals no discernible trend, aligning with the notion that wars are sporadic events without temporal regularity.

Implications and Future Directions

This research bears significant implications for both theoretical and practical realms. The approach delineates a more robust framework for analyzing historical conflict data, thereby reshaping understanding of global conflict risks. The paper emphasizes the dangers of underestimating extreme events, where even a single occurrence could carry devastating impacts, especially in a modern interconnected world.

The findings encourage further exploration of the methodologies employed, particularly in areas where bounded yet extreme phenomena are present, such as financial crises or natural disasters. Future developments in AI could leverage the dual-distribution approach to enhance predictive models and risk assessments, offering more nuanced insights into complex systems characterized by rare but catastrophic events.

In conclusion, Cirillo and Taleb's research into the statistical properties and tail risks of violent conflicts advances the comprehension of warfare dynamics across centuries. Their work challenges existing paradigms and presents a sophisticated narrative on how extreme event risk is not diminishing, urging caution and continuous scholarly engagement with historical data to better understand the possible futures of global conflicts.