## The Power Law of Terrorism

Research result #1: “A Generalized Fission-Fusion Model for the Frequency of Severe Terrorist Attacks,” by Aaron Clauset and Frederik W. Wiegel.

Plot the number of people killed in terrorists attacks around the world since 1968 against the frequency with which such attacks occur and you’ll get a power law distribution, that’s a fancy way of saying a straight line when both axis have logarithmic scales.

The question, of course, is why? Why not a normal distribution, in which there would be many orders of magnitude fewer extreme events?

Aaron Clauset and Frederik Wiegel have built a model that might explain why. The model makes five simple assumptions about the way terrorist groups grow and fall apart and how often they carry out major attacks. And here’s the strange thing: this model almost exactly reproduces the distribution of terrorists attacks we see in the real world.

These assumptions are things like: terrorist groups grow by accretion (absorbing other groups) and fall apart by disintegrating into individuals. They must also be able to recruit from a more or less unlimited supply of willing terrorists within the population.

Research Result #2: “Universal Patterns Underlying Ongoing Wars and Terrorism,” by Neil F. Johnson, Mike Spagat, Jorge A. Restrepo, Oscar Becerra, Juan Camilo Bohorquez, Nicolas Suarez, Elvira Maria Restrepo, and Roberto Zarama.

In the case of the Iraq war, we might ask how many conflicts causing ten casualties are expected to occur over a one-year period. According to the data, the answer is the average number of events per year times 10

^{-2.3}, or 0.005. If we instead ask how many events will cause twenty casualties, the answer is proportional to 20^{-2.3}. Taking into account the entire history of any given war, one finds that the frequency of events on all scales can be predicted by exactly the same exponent.Professor Neil Johnson of Oxford University has come up with a remarkable result regarding these power laws: for several different wars, the exponent has about the same value. Johnson studied the long-standing conflict in Colombia, the war in Iraq, the global rate of terrorist attacks in non-G7 countries, and the war in Afghanistan. In each case, the power law exponent that predicted the distribution of conflicts was close to the value 2.5.

This doesn’t surprise me; power laws are common in naturally random phenomena.

Murk • January 12, 2010 1:59 PM

10^2.3 is closer to 200 than 0.005. I suspect you (or the original) meant 10^-2.3

It doesn’t make much sense to say ‘proportional to a constant’ anyway. It looks like what’s implied is that

number of events is proportional to number of casualties in event to the power of -2.3

Nevertheless, an interesting pattern