Unexpectedly Intriguing!
June 6, 2013

Can the failure of a single, small entity possibly cause the collapse of a much larger entity?

The answer, of course, is yes, provided that the failure of the small entity triggers the release of a greater amount of destructive energy than it took to make it fail. If that release of pent-up destructive energy then triggers the subsequent failure of a larger entity, then the potential for a sustained chain reaction that grows in scale exists. This is called a cascading failure.

It's kind of like dominoes, where a small domino can be set to knock down a larger one, which can then spark off a chain reaction where larger and larger dominoes can be made to fall (HT: PhysOrg).

Here, once the dominoes are lined up and have begun to fall, the only thing that can avoid the collapse of the entire system is an active intervention that creates a gap to interrupt the systemic failure.

That's kind of like how a crime wave can be suppressed in a community through a dramatic increase in police activity after it has started, provided the community wants the crime to stop. Note the parallels to a cascading failure in the basic description below for how a crime wave can take hold in the quoted passage below:

Crime can happen anywhere, but it usually doesn't.

Researchers have noticed that criminal activity seems to be concentrated in self-perpetuating hotspots. Crime leads to more crime. Then, from these epicenters, crime spreads outward through the community.

Mathematicians have a model they've used to study this kind of behavior. It's called a reaction-diffusion-advection system, and criminologists have found it a useful way to analyze issues like "near-repeat victimization" – the observation that single neighborhoods, and even single households, see a disproportionate share of crime.

What criminologists Nancy Rodríguez, Lenya Ryzhik and Henri Berestycki have recently found however is that whether a crime wave can propagate itself depends greatly upon the attitude that the people within the community have with respect to crime itself.

Here, if a community is "pro-crime" or is neutral toward crime, or rather, when a community is not positively supportive of law enforcement, a crime wave cannot be suppressed once it has begun. But if the community is opposed to crime, or is positively supportive of law enforcement, then the crime wave can be arrested, provided a large enough intervention can be deployed to create a gap in the criminal activity. It all comes down to the prevailing choice of the community.

This choice is significant, because a crime wave spreading through a pro-crime population can't be entirely stopped. You end up, Rodríguez said, "always having crime everywhere."

The news is nearly as bad when the population has a neutral attitude toward crime. Although crime primarily persists in hotspots, waves of crime are just as unstoppable.

But if the population has an overall anti-crime stance – meaning that the population is more reluctant to engage in criminal activity – two outcomes are possible. High crime rates can spread, but so can waves of zero criminal activity. And, unlike in the other scenarios, high crime rates can be stopped by adding in a "gap."

In the world of the model, the gap is a stretch of space where the incentive to commit a crime is zero. This corresponds to real-life disincentives to commit crimes, such as an increased police presence, with longer gaps representing more anti-crime efforts.

Rodríguez found that a long enough gap – a large enough police crackdown, for instance – will completely contain a crime outbreak.

The same logic applies toward financial systems, where the only thing that prevents an economic collapse from occurring after the failure of a small entity is the trust that people have in government and financial institutions for the interventions they might undertake to create sufficient gaps in the financial system to prevent the small failure from propagating into a wide-scale one.

If people increasingly distrust those institutions, then the risk of a cascading failure grows, because the interventions that might otherwise be effective in arresting a series of failures after they have begun would be rendered impotent.

That, more than anything else, is what is at stake in the abuse of power scandals and increase in crony capitalism in Washington D.C. Or for that matter, in the ongoing economic crises within the European Union.

In both cases, we'll only know if the balance has been tipped from stability toward instability as once-small failures can no longer be contained from spreading to cause larger and larger failures.

Elsewhere on the Web

The WSJ reports that the Bank of International Settlements may have finally discovered how to create the needed gap to keep the failure of a "too-big-too-fail" bank (ala Lehman Brothers) from collapsing the entire financial system.

Update 7 June 2013: A sharp-eyed reader points us directly to the BIS study.

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