You are currently browsing the tag archive for the ‘power laws’ tag.

Another piece that should be posted in every Federal department office and Parliament House.  Tyler Cowan argues that politicisation, not the markets per se, is the root cause of the current financial troubles.  Bad policies, bad regulation and political interference in the market mechanism led banks and organisations such as GM being ‘too big to fail’: they were propped up and protected from market realities.  Further interference is not the solution.

Today we have a financial-regulatory complex, and it has meant a consolidation of power and privilege. We’ve created a class of politically protected “too big to fail” institutions, and the current proposals for regulatory reform further cement this notion. Even more worrying, with so many explicit and implicit financial guarantees, we are courting a bigger financial crisis the next time something major goes wrong.

We should stop using political favors as a means of managing an economic sector.

Financial markets are subject to criticality—and so catastrophe and collapse—just as a natural system.  Preventing small failures—including through political favours and protecting interest groups—inevitably leads to more pent up energy and catastrophes.  Good system design allows constant small failures, as in an efficient market.  And even those ‘too big to fail’ must be allowed to fail, naturally—or some means found to bleed off the criticality, and reduce their size—else risk complete catastrophe.

MIT’s Technology Review reports a prediction by Didier Sornette and colleagues (Bastiaensen, Cauwels et al. 2009) that a Chinese stock market collapse is imminent–due before 27 July, in fact.

Crashes in stock markets represent cases of self-organised criticality (see, for example, Turcotte 1999): like avalanches, pressure builds in the system to the point where overloading triggers a collapse.  We cannot predict exactly when a collapse will occur, where, or how large the collapse will be, but collapses are inevitable–and sometimes small collapses trigger much larger cascades.  The behaviour of such systems over time follows a scale law: large collapses are few; small collapses are many.

Examples of self-organised criticality can be found in a wide range of natural and social systems, including finance and war (Turcotte and Rundle 2002).  Can we apply the same ideas to nuclear proliferation?

For example, we can substitute the idea of nuclear latency–the level of capability that would allow a swift transition to nuclear status, including through indigenous civilian programs–for load.  (The analogous component in other systems would be combustible material for forest fires, tectonic stress for earthquakes, and over-investment in financial systems.)    The load builds to a point where breakout is inevitable.   But the characteristics of criticality apply: we don’t know when, or where, such a breakout will occur, or how large the ‘avalanche’ will be–one or two nations, for example, or a cascade of proliferation.

What triggers collapse in such a system?  It cannot be capability alone.  But proliferation comprises a combination of material, expertise, infrastructure and intent.  As underlying capability–material, infrastructure and expertise–grows, then intent becomes increasingly important in assessing proliferation risks and behaviour.

And intent necessarily becomes a function of expectation: what are the expected consequences; and what are actors’ expectations of each other?   As in the market, we lack perfect information.  The differences between intent, expectation and surety generate instabilities, which as the load increases and system stress increases, increase the likelihood of collapse.

Moreover, the longer stresses in the system build, the more likely the collapse will be large, cascading as nations with high latency succumb to pressure generated by uncertainties of over others’ intent.

Can we adopt Sornette’s ideas for predicting collapse?  Sornette looks for bubbles in market data; no similar information is available–as far as I’m aware–on nuclear material, industry, or skills.  It’s not exactly the most open of industries–and even more so where there is a covert intent to proliferate.  And even in market data, finding bubble-like behaviour does not necessarily translate into collapses.

But then, Sornette et al do not rely on data alone, but seek to find drivers of such behaviour.  From the Technology Review piece again:

The telltale sign of a bubble, he says, is a faster than exponential growth rate caused by a positive feedback mechanism that generates this nonlinear growth.

Within nuclear proliferation, such drivers include

  • protective hedging against Western conventional dominance, and increasingly, against regional competitors; and
  • increased means of gaining the material, expertise and equipment needed for proliferation, including through sub-national means such as the AQ Khan network.

From a systems perspective there exist drivers trending towards proliferation. Taking the pressure out of the system requires adjusting or defusing the drivers, such as increased transparency of programs; redirecting intent, such as through cooperative security and international regimes; or some sort of as yet unknown technological solution.  The international community has tried a number of these, but given the increasing latency, new and different means may be needed: the barriers suitable for small avalanches, for example, are unlikely to be able to hold back large avalanches.  And therein lies a further problem for the international community: the more the system is held back, and pressure/latency allowed to build rather than being diffused or bled out, the greater the likelihood of a large, cascading breakout.


Bastiaensen, K., P. Cauwels, et al. (2009). “The Chinese Equity Bubble: Ready to Burst.” arXiv: 0907.1827.

Turcotte, D. L. (1999). “Self-organized criticality.” Reports on Progress in Physics 62(10): 1377-1429.

Turcotte, D. L. and J. B. Rundle (2002). “Self-organized complexity in the physical, biological, and social sciences.” Proceedings of the National Academy of Sciences of the United States of America 99: 2463-2465.

Sean Gourley and colleagues developed and analysed a large data set of attacks and casualties across a number of conflicts looking for commonalities.  Gourley provided a brief overview of his work at TED recently:

Analysis of the data revealed a power-law, whereby the probability of an attack of resulting in x number of casualties equals a constant multiplied by x raised to the power of -α.  This points to an underlying structure to armed conflict, where moderated by the coefficient α.  Gourley et al argue that α reflects the organisational structure of the insurgency.  Values above 2.5 indicate a fragmented structure; values below 2.5 reflect a more consolidated structure.

Finding power laws in such data is not unexpected: there are many attacks with few casualties and few attacks with high number of casualties.  I looked at not dissimilar data, from different sources, a few years ago.

The ‘so what’ questions remains, as Gourley acknowledges.

Gourley et al considered the effects of the Iraqi surge.  They believed that consolidation at least offered the opportunity to negotiate with a group, and expected the surge to assist with consolidation.  In the event, under the surge groups initially did seem to coalesce, but then fragmented again.

A few points:

  • these results are robust across different conflicts, but each still has its own peculiarities, and while at a system-level, and over time, outcomes are consistent, it may be easily perturbed at a micro-level;
  • we don’t know what influences, or how to influence, insurgent (or non-state actors or mob) organisational dynamics to an outcome we want;
  • conflict is not a closed system, but open to a range of outside and transitional influences;
  • insurgent groups will interact and co-evolve with each other.  Perhaps there is some sub-system grouping that needs to be taken into account; and
  • technology will act as a mediator on the conflict, the nature and rate of fatalities, and insurgent group behaviour as well.

Last, the benefits or otherwise of coalesence versus fragmentation is contextual.  It is true that ending a civil war via negotiation depends on having someone, representative of the insurgency, with whom to negotiate, and that can be hard to achieve.  The emergence of such a party probably depends as much on dynamics internal to the insurgency as on external pressure.  Once achieved, such a position of strength may not translate easily into a willingness to negotiate.  But civil wars also often simply peter out, as the parties lose will, energy and resources.  When that happens, fragmentation may indicate such a transition.

So the results are of interest, but there is a way to go to generate some further insights and understandings.  I do note that Gourley’s group has been applying their ideas and findings to other areas; there may be some transfer back into the realm of conflict.


Collier, P. and N. Sambanis (2002). “Understanding Civil War: A New Agenda.” The Journal of Conflict Resolution 46(1): 3-12.

August 2020