The Duck of Minerva

The Duck Quacks at Twilight

The Mathematics of War, Revisited

July 15, 2009

A few months back I wrote a post discussing Sean Gourley’s TED talk on the Mathematics of War; specifically, noting that his finding (a power-law distribution of attack frequency and severity in Iraq) was—well—old news. This set off an excellent discussion on Sean’s work, my comments, and more generally how the social and hard sciences can clash. More recently, Tom Ricks of The Best Defense blog revisited Sean’s talk with his own skepticism, which induced a response from Sean, and further skepticism by Ricks. In defense of his work, Sean responded to Tom’s post with the following:

With this new approach we can do several important things that were not possible before. We can understand the underlying structure of an insurgency i.e. how an insurgency ‘decides’ to distribute its forces (weapons, people, money etc). Further, we can explain why this kind of insurgent structure emerges in multiple different conflict zones around the world. We can estimate the number of autonomous insurgent groups operating within a theatre of war. We can monitor and track a conflict through time to see how either sides strategies are affecting the state of the war. Finally we can compare the mathematical patterns of current ongoing wars with past wars to estimate how close they are to ending.

I think Sean’s work in extremely important, as in many ways our research interests run parallel and this project has great potential. That said, his response leaves me with more questions than answers, therefore, with Sean’s response in hand I would like to revisit the mathematics of war.

First, I have serious doubts as to the connection between the distribution of attack frequency and severity and the underlying structure of an insurgency. Power-law distributions can provide a categorical approximation of a network’s underlying structure because in these cases the distribution in question refers to the frequency of edge counts among nodes, a structural measurement. Even for networks, however, the actual underlying structures of networks following a power-law can vary wildly. Attack frequencies, on the other hand, have nothing to do with structure. In what way, then, is this metric valid for measuring the structure or distribution of insurgent forces?

There is also a large element of context that is not captured in this analysis. To get to Sean’s question on why different types of insurgencies occur in different parts of the world, with varying lethality and effectiveness, one must account for the inherent variance in ability among insurgents and insurgent organizations. We know that people vary in their abilities to perform any task, which of course includes insurgency; therefore, we must control for any exogenous or endogenous factors that could contribute to this variance as to avoid inserting into our analysis the belief that all insurgent are created equally. Once a reasonable number of theoretically justifiable control variables are identified, we may be able to get at this question at both a micro (insurgent) and macro (insurgency) level. A present, the data used in Sean’s analysis accounts for this variation.

Next, there has been quite a bit of research on the duration of wars, including state-on-state, civil and insurgency. For this research, a critical hurdle has always been how to overcome bias in the data collection and reporting when attempting to approximate how various factor contribute to the curation of a conflict. Sean uses open-scource media accounts of attacks to develop his data, and because most of these media outlets are primarily motivated by profit it is difficult to view this data as unbiased. This problem, however, can be dealt with by various sampling techniques and control varaibles. Of greater concern are the eventual conclusions drawn by attempting to match conflict patterns in this manner. With Sean’s data, we might ask what factors contribute to ending conflicts following a power-law. Unfortunately, as previously discussed, all manner of conflicts follow this pattern. If two conflicts have a near identical power-law distribution when observed in the long term, but upon examination we find that one is an insurgency and other a state-on-state conflict, what insight have we gained? This categorical approach, therefore, may be significantly limited in its explanatory value.

Finally, I must point out that I have a very superficial perspective on Sean’s work, as I have only been exposed to the TED talk, and the discussions that have followed from it. There are likely many elements of this research that I am missing, and as such all of the above concerns may have already been addressed. I am interested in your take on Sean’s response, my position, and where you see the value in this research? To quote Tom, “Smart, statistically-comfortable readers: Do you see support for these claims?”

Photo: Chart of distribution of attacks with magnitude from “Variation of the Frequency of Fatal Quarrels with Magnitude,” by Lewis F. Richardson.

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Drew Conway, CEO and founder of Alluvium, is a leading expert in the application of computational methods to social and behavioral problems at large-scale. Drew has been writing and speaking about the role of data — and the discipline of data science — in industry, government, and academia for several years.