Leyman´s Terms for "From Old Wars to New Wars and Global Terrorism"

Theese are some of the implications of our research. For the paper go to:

http://search.arxiv.org:8081/paper.jsp?p=physics/0506213

What is a power law?

A power-law is a particular type of statistical pattern. It is very different from the more familiar bell curve typically associated with random incidents. The main practical implication of a ‘power-law war’ is that big incidents, i.e. deadly ones, are always quite likely to happen. If the distribution of casualties were a Bell curve rather than a power law, then such big events would be virtually impossible.

A power-law, and its associated power-law index, represents a particularly potent indicator. The presence of a power-law has important practical implications concerning future risk: for example, the risk that future attacks will be of a particular intensity or larger. We are currently building up a toolbox of such indicators in order to fully characterize the spatio-temporal behavior of such incidents and hence fully characterize a war’s evolution and the associated risks.

What exactly did we do in this particular project?

We analyzed incidents in Iraq and Colombia, asking what fraction of incidents have one casualty, two casualties, etc. We then graphed this and looked at the shape. All sorts of shapes are possible but the power-law gives a very close fit for Iraq, for Colombia -- and also for terrorist events in non-G7 countries.

An interesting feature of the mathematics of power-laws, is that it matters little whether we use the number killed or the number killed and wounded: as long as the number killed is a fixed fraction of the number killed and wounded, we will get the same power-law behavior. In addition, the same power-law behavior will arise even if the casualty figures are systematically over- or under-reported by some fixed fraction.

What is the significance of the number 2.5?

Power-laws are characterized by a number called the ‘index’. As the power-law index decreases, the chance of big events increases. Conventional wars have an index of about 1.8. The Iraq war had exactly this index at the beginning when it was a conventional conflict. But over time the index has drifted upwards toward 2.5 as the war itself has become increasingly irregular. This reflects the fact that attacks are coming from small cells which cannot coordinate well with each other because of increasing coalition pressure. By contrast, the power-law index for Colombia has drifted downwards toward 2.5, implying that the guerillas are becoming increasingly centralized and are therefore more able to generate large incidents than before.

Global terrorist events in non-G7 countries also follow a power-law with index equal to 2.5. The implication is that the degree of centralization/coordination in global terrorism is now roughly equivalent to that characterizing insurgency in both Iraq and Colombia. Hence these groups are all quite similar in terms of their structure and operations, irrespective of their original motivations and ideals or their particular field of combat.

What does ‘steady state’ mean?

This simply means a kind of equilibrium where the power-law index tends to neither increase nor decrease over time. If the Colombian armed forces increase their pressure on the guerrillas, one response will be for the guerrillas to regress back to smaller, more elusive units. This would impede the guerrillas’ ability to generate big attacks and hence the power-law index will increase, i.e. it will climb back above 2.5.

What does this tell us about the progress of the war in Colombia?

The news is mixed from the government’s perspective. The downward trend of the power-law index toward 2.5 suggests an enhanced ability of the guerrillas to coordinate, and hence generate, big attacks. This suggests that over the years the guerillas have strengthened their central command lines. At the same time, our results suggest that the guerillas are currently operating in the same way as other non-G7 terrorists -- either by their own design, or because the Colombian army is forcing them to fight in this way through its own military operations. The slight increase in the index over the last few years suggests that turning up the pressure on the guerrillas has caused some fragmentation of their command structures, thereby hindering their ability to coordinate big attacks.