The problem is not with the math. It's a straightforward power function. Please note in the last graph shown that there were huge error bars which means that there was a bit of uncertainty in the data. Without knowing what underlying assumptions they made in constructing their statistical model, it's almost impossible to know whether their model accurately reflects reality or not. I'd have been happier if he'd verified the model using data from past conflicts of a similar nature where the outcomes are known (Vietnam anyone?, quantified by the shades of McNamara and his statisticians). Then again, economists are always modeling human behavior and their models are more often wrong than right. The quants on Wall Street were physicists as well and their one caveat to their financial models was that once humans use the models they alter their behavior because of the model's result (a dynamic feedback loop) thereby rendering the model useless because the underlying parameters (human behavior) have changed (and look how well that turned out). So, one could argue that reading goat entrails for portents and omens might be just as effective an exercise as curve fitting insurgencies, and you get to eat the goat afterwards.

Seriously though, if I were to pursue this line of inquiry, I would ask an evolutionary biologist or someone like Mandelbrot what they think of this. War is like evolution with natural selection to the nth degree, so a decent evolutionary biologist might have some insight here and they know math too. Mandelbrot modeled dynamic systems using Julia sets which are mathematical functions that interactively feedback on themselves. The living world is dynamic, highly interactive, and hence, fractal. Since war is ultimately about living rather than dying, and is very dynamic, one is likely to get more mileage seeing if the underlying mathematics of war are really fractal and currently unfathomable to human comprehension rather than simply a power function. Whether war is Darwinian or not, if any biologist has worked out the math to prove that assumption, he or she isn't saying.

Tom,
It isn't so much that he has nothing, but rather he has nothing new.

We had a wonderful conversation on this talk a few weeks ago, you may find it interesting.

http://www.drewconway.com/zia/?p=577

Cheers!

That's a good discussion on www.drewconway.com
Best,
Tom

The talk purports to discover a power law for conflict—small conflicts in which relatively small numbers of people are killed occur more frequently than large conflicts in which many are killed.

This simply expresses the reality that killing increasingly larger numbers of people becomes increasingly difficult and/or rare, resulting in a crude scale invariance (→ "power law"), so the talk's results are rather unsurprising and trivial. Furthermore, any smooth distribution can be fit to a power law over some range, so the finding is tautologous without some solid technical backing, which so far appears to be absent from the literature.

This crude scale invariance for conflicts was studied by Lewis F. Richardson in "Variation of the Frequency of Fatal Quarrels With Magnitude" [1]. Also relevant is the paper by Clauset et al., "On the Frequency of Severe Terrorist Events" [2]. The difficulties of testing if real data actually does fit a power law are discussed in another paper by Clausen [3]. The full references are:

1. Lewis F. Richardson. Variation of the Frequency of Fatal Quarrels With Magnitude. Journal of the American Statistical Association, Vol. 43, No. 244 (Dec., 1948), pp. 523–546.
2. Clauset, Young, and Gleditsch, On the Frequency of Severe Terrorist Events. Journal of Conflict Resolution, Vol. 51, No. 1, 58-87 (2007).
3. A. Clauset, C. R. Shalizi, and M. E. J. Newman, "Power-law distributions in empirical data" SIAM Review, to appear (2009). (arXiv:0706.1062).

Richardson's figure on page 527 illustrates the "power law" over a narrow range, which is the very nearly linear part of the log-log plot.

It is not at all clear how these limited, aggregate results could be applied to draw conclusions about the state of a specific insurgency at any given time, as the talk does.

This is helpful. It is good to have a readership smarter than I am!
Best,
Tom

I agree that without some comparison of the evolution of Mr. Gourley's alpha parameter over the course of other insurgencies he's got nothing. Either there is really some useful information here and a reproducible pattern can be observed, or this is just another stochastic variable. Also, he never backs up his assertion that alpha reflects the 'structure' of the insurgency. Again, if he repeated his calculations for previous conflicts with well documented changes in the structure of insurgency (fighting between splinter groups, internal power struggles, etc) and showed consistent changes after major realignments, he might have an argument, but at the moment, nothing so illuminating.

BUT, he does have the honesty to admit this is a preliminary look the data and he doesn't know if they can tell us anything useful yet. So I would mostly criticize him for making a fancy presentation well before he has the results to warrant it. Perhaps his grant's almost up and he's desperate for some cash or something.

I think the question to ask (if I understood his implied definition of structure of the insurgent groups) is can we do something to make the insurgent groups smaller or larger, since that seems to be the driver of their ability to fight effectively.

I'm sure the Pentagon will give him a big grant to work on this so they will have stuff for news conferences.