A power law describes a relationship between 2 quantities, typically between event frequency and event size where the larger the event, the smaller the frequency. (Think of a long-tail distribution) Recently, large events have been referred to as black swans, rare large improbable events (Talub, 2007). Predicting black swans is difficult because there are too many variables and unknowns in prediction, but their effect size make them too problematic to ignore.
The Physics arXiv Blog recent discussed a proposition by Didier Sornette at the Swiss Federal Institute of Technology. Sornette says that outsized outliers are more common then they should be in power distributions because they are subject to feedback loops. He termed these outliers dragon kings. In real life examples (at lest it seems to me that) these feedback loops seem to often be social; an example of jumping on the bandwagon. This is another reason that black swans are much more common than they should be according to power laws.
Very relevant for risk management calculations. If you are preparing for potential risks, beware not only for black swans (rare events with large effects that are hard to predict because you don’t know the future of many varibles), but also for dragon kings (feedback loops that increase the effect size of somewhat rare events, making them more common that a power law distribution would expect). It provides a rationale for the development of resilient organizations, the ability to change quickly in response to environmental events, instead of relying on cost probability decision matrixes.