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# A Few Facts About Small Probabilities

“The earthquake and tsunami we had last week both exceeded our engineering assumptions by a long shot….The nuclear industry around the world probably will have to review how we set those assumptions in designing a nuclear power plant.”

Thoughts from Nicolas Taleb:

The Japanese Nuclear Commission had the following goals set in 2003: “The mean value of acute fatality risk by radiation exposure resultant from an accident of a nuclear installation to individuals of the public, who live in the vicinity of the site boundary of the nuclear installation, should not exceed the probability of about 1×10^6 per year (that is, at least 1 per million years)”.

That policy was designed only 8 years ago. Their one in a million-year accident occurred about 8 year later. We are clearly in the Fourth Quadrant there.

I spent the last two decades explaining (mostly to finance imbeciles, but also to anyone who would listen to me) why we should not talk about small probabilities in any domain. Science cannot deal with them. It is irresponsible to talk about small probabilities and make people rely on them, except for natural systems that have been standing for 3 billion years (not manmade ones for which the probabilities are derived theoretically, such as the nuclear field for which the effective track record is only 60 years).

1. Small probabilities tend to be incomputable; the smaller the probability, the less computable. (Forget the junk about “Knightian” uncertainty, all small probabilities are incomputable).
2. Model error causes the underestimation of small probabilities & their contribution (on balance, because of convexity effects). Any model error, just as any undertainty about flying time causes the expected arrival to be delayed (you rarely land 4 hours early, more often 4 hours late on a transatlantic flight, so “unforeseen” disturbances tend to delay you). See my argument about second order effects with my paper. [INTUITION: uncertainty about the model used for calculation of random effects causes a second layer of randomness, causing small probabilities to rise on balance].
3. The problem is more acute in Extremistan, particularly the manmade part. The probabilities are undestimated but the consequences are much, much more underestimated.
4. As I wrote, because of globalization, the costs of natural catastrophes are increasing in a nonlinear way.
5. Casanova problem (survivorship bias in probability): If you compute the frequency of a rare event and your survival depends on such event not taking place (such as nuclear events), then you underestimated that probability. See the revised note 93 on αδηλων.
6. Semi-technical Example: to illustrates the point (how models are Procrustean beds):
 Still curious? Taleb is the author of The Black Swan and The Bed of Procrustes.

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