The Black Swan: The Impact of the Highly Improbable

The second, and more vicious, variety of the problem of silent evidence is as follows. When I was in my early twenties and still read the newspaper, and thought that steadily reading the newspapers was something useful to me, I came across an article discussing the mounting threat of the Russian Mafia in the United States and its displacement of the traditional Louie and Tony in some neighborhoods of Brooklyn. The article explained their toughness and brutality as a result of their being hardened by their Gulag experiences. The Gulag was a network of labor camps in Siberia where criminals and dissidents were routinely deported. Sending people to Siberia was one of the purification methods initially used by the czarist regimes and later continued and perfected by the Soviets. Many deportees did not survive these labor camps.

Hardened by the Gulag? The sentence jumped out at me as both profoundly flawed (and a reasonable inference). It took me a while to figure out the nonsense in it since it was protected by cosmetic wrapping; the following thought experiment will give the intuition. Assume that you’re able to find a large, assorted population of rats: fat, thin, sickly, strong, well-proportioned, et cetera. (You can easily get them from the kitchens of fancy New York restaurants.) With these thousands of rats, you build a heterogeneous cohort, one that is well representative of the general New York rat population. You bring them to my laboratory on East Fifty-ninth Street in New York City and we put the entire collection in a large vat. We subject the rats to increasingly higher levels of radiation (since this is supposed to be a thought experiment, I am told that there is no cruelty in the process). At every level of radiation, those that are naturally stronger (and this is the key) will survive; the dead will drop out of your sample. We will progressively have a stronger and stronger collection of rats. Note the following central fact: every single rat, including the strong ones, will be weaker after the radiation than before.

An observer endowed with analytical abilities, who probably got excellent grades in college, would be led to believe that treatment in my laboratory is an excellent health-club replacement, and one that could be generalized to all mammals (think of the potential commercial success). His logic would run as follows: Hey, these rats are stronger than the rest of the rat population. What do they seem to have in common? They all came from that Black Swan guy Taleb’s workshop. Not many people will have the temptation to go look at the dead rats.

Next we pull the following trick on The New York Times: we let these surviving rats loose in New York City and inform the chief rodent correspondent of the newsworthy disruption in the pecking order in the New York rat population. He will write a lengthy (and analytical) article on the social dynamics of New York rats that includes the following passage: “Those rats are now bullies in the rat population. They literally run the show. Strengthened by their experience in the laboratory of the reclusive (but friendly) statistician/philosopher/trader Dr. Taleb, they …”

Vicious Bias

There is a vicious attribute to the bias: it can hide best when its impact is largest. Owing to the invisibility of the dead rats, the more lethal the risks, the less visible they will be, since the severely victimized are likely to be eliminated from the evidence. The more injurious the treatment, the larger the difference between the surviving rats and the rest, and the more fooled you will be about the strengthening effect. One of the two following ingredients is necessary for this difference between the true effect (weakening) and the observed one (strengthening): a) a degree of inequality in strength, or diversity, in the base cohort, or b) unevenness, or diversity, somewhere in the treatment. Diversity here has to do with the degree of uncertainty inherent in the process.

More Hidden Applications

We can keep going with this argument; it has such universality that once we get the bug it is hard to look at reality with the same eyes again. Clearly it robs our observations of their realistic power. I will enumerate a few more cases to illustrate the weaknesses of our inferential machinery.