« The future of terrorism | Main | Why I think the iPad is good »

January 25, 2010

On the frequency of severe terrorist attacks; redux

Sticking with the theme of terrorism, in the new issue of the Journal of Conflict Resolution is an article by Frits Wiegel and me [1], in which we analyze, generalize, and discuss the Johnson et al. model on the internal dynamics of terrorist / insurgent groups [2].

The goal of the paper was to (i) relax one of the mathematical assumptions Johnson et al. initially made when they introduced the model back in 2005, (ii) clearly articulate its assumptions and discuss the evidence for and against them, (iii) discuss the relevance of the model for counter-terrorism / counter-insurgency policies, and (iv) identify ways the model's assumptions and predictions could be tested using empirical data.

Here's the abstract:

We present and analyze a model of the frequency of severe terrorist attacks, which generalizes the recently proposed model of Johnson et al. This model, which is based on the notion of self-organized criticality and which describes how terrorist cells might aggregate and disintegrate over time, predicts that the distribution of attack severities should follow a power-law form with an exponent of alpha=5/2. This prediction is in good agreement with current empirical estimates for terrorist attacks worldwide, which give alpha=2.4 \pm 0.2, and which we show is independent of certain details of the model. We close by discussing the utility of this model for understanding terrorism and the behavior of terrorist organizations, and mention several productive ways it could be extended mathematically or tested empirically.

Looking forward, this paper is really just a teaser. There's still a tremendous amount of work left to do both in terms of identifying other robust patterns in global terrorism and in terms of explaining where those patterns come from. The hardest part of this line of research promises to be reconciling traditional economics-style assumptions in conflict research (that terrorists are perfectly rational actors: their actions are highly strategic, are best explained using game theory, and are otherwise contingent on the particular local history and politics) with these newer physics-style assumptions (that terrorists are highly irrational "dumb" actors: their actions blindly follow fundamental "laws", are best explained using simple mechanical models, and are otherwise random). The truth is almost surely a compromise between these two extremes, one that includes both local strategic flexibility and contingency, along with fundamental constraints created by the "physics" of planning and carrying out terrorist attacks. Developing a theory that captures the right amount of both approaches seems hard, but exciting.


[1] A. Clauset and F. W. Wiegel. "A generalized aggregation-disintegration model for the frequency of severe terrorist attacks." Journal of Conflict Resolution 54(1): 179-197 (2010). (arxiv version)

[2] This model should now perhaps be called the Bohorquez et al. model, since that's the author order for their published version, which appeared last month in Nature. See also the accompanying commentary in Nature, in which I'm quoted.

posted January 25, 2010 03:18 PM in Terrorism | permalink


One could always come up with a clever name for the model. :)

The random walker rankings were actually referred to only as the "monkey ranking system" in one person's SIAM Review article without explaining what that actually meant (my fault, and there is indeed a story or at least a snarky remark behind the origin for that). Then there are also unofficial names, which for that one include "PMS" (for "Peter Mucha System"; Peter wouldn't let us use that one in publications). And things like "sniper bifurcations" have even come into standard usage.

Posted by: Mason Porter at January 25, 2010 05:52 PM

Just wait to I get some evolutionary game theory / social-learning models out there. Mixes elements of both, I think.

Posted by: Matt Zimmerman at January 25, 2010 09:09 PM

@Mason: PMS... that's too great to not try to work into a paper somewhere. You could always write a paper without Peter in which you refer to his system as PMS, since he can't veto then. For the kind of model I'm ultimately thinking of for violent human conflict, maybe I'll call it something like "DUMB Agents; Smart System" (aka DUMBASS)...

@Matt: I would love to have some more company in this field, and I'd love to see what evolutionary game theory / social learning can do for striking the right balance.

Posted by: Aaron at January 26, 2010 08:32 AM

That's true; I could do that. And it would be fair, too, as the original idea was his.

If you still have the polar coordinate dendrogram code I sent you, you might want to check if the commented-out sections therein still contain a rather snarky name for the color scheme that goes with our Congressional committee papers. (I don't remember if it was deleted by that point.)

Posted by: Mason at January 27, 2010 03:47 AM