I don't know what I know I don't know.... or something

I just finished reading a very interesting book for my Insurance Law Seminar. The book is The Black Swan, by Nassim Taleb.

Basically, the book centers around the notion of the black swan, the random event that cannot be modeled for in risk analysis or econometric projections, because by definition it does not exist within Gaussian (bell curve) models.

The book starts with a distinction between what the author dubs mediocristan and extremistan. The former is the world in which Gaussian bell curve models can accurately forecast results, because no single variant can affect the mean. The latter, extremistan, cannot be based on Gaussian modeling, because a single variant can affect the mean. To give an example, if you lined 100 people up, the average height would be something like 5'10. But then if you added to the list the most extreme variable you could imagine, in this case the tallest man in the world, you would not be able to move the mean beyond an insignificant amount. The reason is because height is a feature that exists entirely within mediocristan. It fits inside the Gaussian bell curve, and we can model for and predict it. Even if you throw the crazy variable of world's tallest man into your 100 person sample, you will not deviate from the mean, and the bell curve projection will be stable.

On the other hand, if you lined up 100 people and ranked their net worth, you would get something like $100,000 on average for an American. However, if you added the richest man in the world to this list, Bill Gates, you would deviate the mean so much that the sample would drastically change. This is because wealth is a function of extremistan, or a feature which exists outside of Gaussian modeling. In other words, the variables of things that exist within extremistan (wealth, insurance losses, stock performance) are so extreme that you cannot actually model for them, and as a result, any attempt to do so will result in worthless forecasts.

With this basic premise, the author delves into the world of risk management, finance, and insurance. He then gives examples of how we as humans are foolish because we like to think we live in a Gaussian world, one in which variables can be modeled. He then gives countless examples of how everyone from economists to political theorists to market predictors to doctors, etc., are all collectively terrible at predicting. And yet, despite countless doctors, banks, economists, trading firms, and other 'experts' doling out horrible predictions every year, we keep lining up like suckers at the trough to take in next years projections. Taleb calls this the narrative fallacy, our need to fit a story or pattern to a series of connected or disconnected facts.

One particularly interesting example was of a social experiment that statisticians discovered that proves how overconfident we generally are about things we know nothing about. In the experiment a group of subjects are asked a random factual question, such as what is the population of Moscow, Russia? The subjects are asked to give their answer in the form of a range, any range they want, with the caveat that they must be 98% sure that the correct answer lies within that range. Incredibly, when this experiment was first conducted at the Harvard Business School among students, the error rate among the ranged responses was an astounding 45%! Incredibly, the Harvard business students were so wildly over-confident in their ability to estimate within a 98% accurate range of answers, that their over-confidence caused them to not only incorrectly guess the answer, but wildly so. The point being that not only do we not know very much, but more importantly, we don't know what we don't know.

Finally, the book turns to the world of investment and insurance underwriting, and not surprising, the results there are just as bad. By the time you are finished reading the book, you will have lost all confidence in any numeric estimation or evaluation of future events beyond five minutes from now.