Tag Archives: power laws

Applying Earthquake Physics to Conflict Analysis

I’ve long found the analogies between earthquakes and conflicts intriguing. We often talk of geopolitical fault lines, mounting tensions and social stress. “If this sounds at all like the processes at work in the Earth’s crust, where stresses build up slowly to be released in sudden earthquakes … it may be no coincidence” (Buchanan 2001).

To be sure, violent conflict is “often like an earthquake: it’s caused by the slow accumulation of deep and largely unseen pressures beneath the surface of our day-to-day affairs. At some point these pressures release their accumulated energy with catastrophic effect, creating shock waves that pulverize our habitual and often rigid ways of doing things…” (Homer-Dixon 2006).

But are fore shocks and aftershocks in social systems really as discernible as well? Like earthquakes, both inter-state and internal wars actually occur with the same statistical pattern (see my previous blog post on this). Since earthquakes and conflicts are complex systems, they also exhibit emergent features associated with critical states. In sum, “the science of earthquakes […] can help us understand sharp and sudden changes in types of complex systems that aren’t geological–including societies…” (Homer-Dixon 2006).

The Model

To this end, I collaborated with Professor Didier Sornette and Dr. Ryan Woodard from the Swiss Federal Institute of Technology (ETHZ) to assess whether a mathematical technique developed for earthquake prediction might shed light on conflict dynamics. I presented this study along with our findings at the American Political Science Association (APSA) convention last year (PDF).

This geophysics technique, “superposed epoch analysis,” is used to identify statistical signatures before and after earthquakes. In other words, this technique allows us to discern whether any patterns are discernible in the data during foreshocks and aftershocks.

Earthquake physicists work from global spatial time series data of seismic events to develop models for earthquake prediction. We used a global time series dataset of conflict events generated from newswires over a 15-year period. The graph below explains the “superposed epoch analysis” technique as applied to conflict data.


The curve above represents a time series of conflict events (frequency) over a particular period of time. We select arbitrary threshold, such as “threshold A” denoted by the dotted line. Every peak that crosses this threshold is then “copied” and “pasted” into a new graph. That is, the peak, together with the data points 25 days prior to and following the peak is selected.

The peaks in the new graph are then superimposed and aligned such that the peaks overlap precisely. With “threshold A”, two events cross the threshold, five for “threshold B”. We then vary the thresholds to look for consistent behavior and examine the statistical behavior of the 25 days before and after the “extreme” conflict event.


For this study, we performed the computational technique described above on the conflict data for the US, UK, Afghanistan, Columbia and Iraq.

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The foreshock and aftershock behaviors in Iraq and Afghanistan appear to be similar. Is this because the conflicts in both countries were the result of external intervention, i.e., invasion by US forces (exogenous shock)?

In the case of Colombia, an internal low intensity and protracted conflict, the statistical behavior of foreshocks and aftershocks are visibly different from those of Iraq and Afghanistan. Do the different statistical behaviors point to specific signature associated with exogenous and endogenous causes of extreme events? Does one set of behavior contrast with another one in the same way that old wars and new wars differ?

Future Research

Are certain extreme events endogenous or exogenous in nature? Can endogenous or exogenous signatures be identified? In other words, are extreme events just part of the fat tail of a power law due to self-organized criticality (endogeneity)? Or is catastrophism in action, extreme events require extreme causes outside the system (exogeneity)?

Another possibility still is that extreme events are the product of both endogenous and exogenous effects. How would this dynamic unfold? To answer these questions, we need to go beyond political science.

The distinction between responses to endogenous and exogenous processes is a fundamental property of physics and is quantified as the fluctuation-dissipation theorem in statistical mechanics. This theory has been successfully applied to social systems (such as books sales) as a way to help understand different classes of causes and effects.

Our goal is to use the same techniques to investigate the questions: Do conflict among actors in social systems display measurable endogenous and exogenous behavior?  If so, can a quantitative signature of precursory (endogenous) behavior be used to help recognize and then reduce growing conflict? The next phase of this research will be to apply the above techniques to the conflict dataset already used to examine the statistical behavior of foreshocks and aftershocks.

The Mathematics of War: Before the TED Talk

My new colleague Sean Gourely recently presented his research on “The Mathematics of War” at the TED 2009 conference. I met Sean in March this year, a month after TED, and soon realized we had been doing very similar research on the mathematics of war. Indeed, I carried out related research with Dr. Ryan Woodard while at the Santa Fe Institute (SFI) exactly three years ago, in June 2006.

However, the discovery that conflict follows a power law distribution was actually made by another physicist, Lewis Fry Richardson, some 60 years ago. A power law distribution relates the frequency and “magnitude” of events. For example, the Richter scale, relates the size of earthquakes to their frequency. Richardson found that the frequency of international wars and the number of casualities each produced followed a power law.

Before TED

More recently, my colleague Erik-Lars Cederman sought to explain Richardson’s findings in his 2003 peer-reviewed publication “Modeling the Size of Wars: From Billiard Balls to Sandpiles.” However, Lars used an invalid statistical technique to test for power law distributions.

In 2005, I began collaborating with Professors Neil Johnson and Michael Spagat on related research after I came across their fascinating co-authored study that tested casualty distributions in new wars (internal conflicts) for power laws. Turns out Sean also collaborated with Neil and Michael on the research he presented at TED, but he was not a co-author on the 2005 study, which explains why we only met 4 years later.

In any case, I invited Michael to present his research at The Fletcher School in the Fall of 2005 to generate interest here. Shortly after, I suggested to Michael that we test whether conflict events, in addition to casualties, followed a power law distribution. I had access to an otherwise proprietary dataset on conflict events that spanned a longer time period than the casualty datasets that he and Neils were working off. I also suggested we try to test whether casualties from natural disasters follow a power law distribution.

We chose to pursue the latter first and I submitted an abstract to the 2006 American Political Science Association (APSA) conference to present our findings. Soon after, I was accepted to the Santa Fe Institute’s Complex Systems Summer Institute for PhD students and took the opportunity to pursue my original research in testing conflict events for power law distributions with my colleague Dr. Woodard.

Disaster Casualties

The APSA paper, presented in August 2006, was entitled “Natural Disasters, Casualties and Power Laws:  A Comparative Analysis with Armed Conflict” (PDF). Here is the paper’s abstract and findings:

Power-law relationships, relating events with magnitudes to their frequency, are common in natural disasters and violent conflict. Compared to many statistical distributions, power laws drop off more gradually, i.e. they have “fat tails”. Existing studies on natural disaster power laws are mostly confined to physical measurements, e.g., the Richter scale, and seldom cover casualty distributions. Drawing on the Center for Research on the Epidemiology of Disasters (CRED) International Disaster Database, 1980 to 2005, we find strong evidence for power laws in casualty distributions for all disasters combined, both globally and by continent except for North America and non-EU Europe. This finding is timely and gives useful guidance for disaster preparedness and response since natural catastrophes are increasing in frequency and affecting larger numbers of people.  We also find that the slopes of the disaster casualty power laws are much smaller than those for modern wars and terrorism, raising an open question of how to explain the differences. We show that many standard risk quantification methods fail in the case of natural disasters.


Conflict Casualties

Dr. Woodard and I presented our research on power laws and conflict events at SFI in June 2006. We produced a paper in August of that year entitled “Concerning Critical Correlations in Conflict, Cooperation and Casualties” (PDF). As the title implies, we also tested whether cooperative events followed a power law. As far as I know, we were the first to test conflict events not to mention cooperative events for power laws. In addition, we looked at conflict/cooperation (C/C) events in Western countries.

The abstract and some findings are included below:

Knowing that the number of casualties of war are distributed as a power law and given a rich data set of conflict and cooperation (C/C) events, we ask: Are there correlations among C/C events? Is there a correlation between C/C events and war casualties? Can C/C data be used as proxy for (potentially) less reliable casualty data? Can C/C data be used in conflict early warning systems? To begin to answer these questions we analyze the distribution of C/C event data for the period 1990–2004 in Afghanistan, Colombia, Iran, Iraq, North Korea, Switzerland, UK and USA. We find that the distributions of individual C/C event types scale as power laws, but only over approximately a single decade, leaving open the possibility of a more appropriate fit (for which we have not yet tested). However, the average exponent of the power law (2.5) is the same as that found in recent studies of casualties of war. We find low levels of correlations between C/C events in Iraq and Afghanistan but not in the other countries studied. We find that the distribution of the sum of all conflict or cooperation events scales exponentially. Finally, we find low levels of correlations between a two year time series of casualties in Afghanistan and the corresponding conflict events.


Next Steps

Sean and I are hoping to collaborate in future research as there is still a lot of interesting work to be done in this area. In the meantime, however, we’re collaborating on Ushahidi’s Swift River, for which I recently developed a very basic pseudo code to score the veracity of incident reports.

Meeting Sean has reminded me just how interested and involved I was in the above research 3-4 years ago. While I haven’t pursued the power law research since, I did continue working with Dr. Woodard and produced another study last year on the application of geophsyics analysis to conflict data to identify for shocks and aftershocks in major conflicts. This will be the subject of my next blog post.