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Okay, let’s try to elect the mediocre thinking to a higher level and see what it is that constitutes the human understading of the world. Or rather, what it is that doesn’t. But, isn’t that a bit too enthousiastic, one might ask?! Well, it depends who you ask I guess.

Nassim Taleb, a Greek amongst the Romans, explains this quite eloquently by referring to an inherent psychological blindness, what he calles the Platonic fallacy. While merely referring to the great Plato his ‘Ideas’ idea, Taleb really means wih this the focus on those pure, well-defined, and easily discernible objects like triangles, or more social notions like friendship or love, at the cost of ignoring those objects of seemingly messier and less tractable structures.

In other words, he uses it to show the idea that reality is not compelled to be what theories want it to be. Reality is complex, changing and is not always amenable to narrowly focused technical models.

Then he argues that it leads to three distortions in our understanding of the world:

He also believes that people are subject to the triplet of opacity, through which history is distilled even as current events are incomprehensible. The triplet of opacity consists of:

1. an illusion of understanding of current events
2. a retrospective distortion of historical events
3. an overestimation of factual information, combined with an overvalue of the intellectual elite

Okay, so these ideas are used to see why it is that so many people just don’t fully understand that they don’t understand, especially their own expertise. And why it is that so many people are wrong about so many things in life, including myself of course, but especially the self-proclaimed ‘experts’ when they make predictions about anything social; that includes: economic experts, financial experts, sociologists, psycologists, statisticians, historians, politicians, physicians and even mathematicians. Basically, this applies to anyone who makes a claim to be an expert on any social system, like the economy or the market, or tries to apply the Gaussian probability calculus to predict outcomes of social situations.

I must admit that when it comes to value estimates of social expertise, Taleb has influenced my thinking to a large extent as one might have noticed.

Here a part of one of his essays that he published on Edge.org, together with lots of data about the financial markets, in which he made a matrix to help distinguish between domains in life that are fairly predictable, which he calles ‘Mediocristan’, and those fields which are inherently unpredictable, called ‘Extremistan’.

Read the full article at Edge.org: THE FOURTH QUADRANT: A MAP OF THE LIMITS OF STATISTICS [9.15.08] By Nassim Nicholas Taleb

The Map

Now it lets see where the traps are:

First Quadrant: Simple binary decisions, in Mediocristan: Statistics does wonders. These situations are, unfortunately, more common in academia, laboratories, and games than real life—what I call the “ludic fallacy”. In other words, these are the situations in casinos, games, dice, and we tend to study them because we are successful in modeling them.

Second Quadrant: Simple decisions, in Extremistan: some well known problem studied in the literature. Except of course that there are not many simple decisions in Extremistan.

Third Quadrant: Complex decisions in Mediocristan: Statistical methods work surprisingly well.

Fourth Quadrant: Complex decisions in Extremistan: Welcome to the Black Swan domain. Here is where your limits are. Do not base your decisions on statistically based claims. Or, alternatively, try to move your exposure type to make it third-quadrant style (“clipping tails”).

Two Difficulties

Let me refine the analysis. The passage from theory to the real world presents two distinct difficulties: “inverse problems” and “pre-asymptotics”.

Inverse Problems. It is the greatest epistemological difficulty I know. In real life we do not observe probability distributions (not even in Soviet Russia, not even the French government). We just observe events. So we do not know the statistical properties—until, of course, after the fact. Given a set of observations, plenty of statistical distributions can correspond to the exact same realizations—each would extrapolate differently outside the set of events on which it was derived. The inverse problem is more acute when more theories, more distributions can fit a set a data.

This inverse problem is compounded by the small sample properties of rare events as these will be naturally rare in a past sample. It is also acute in the presence of nonlinearities as the families of possible models/parametrization explode in numbers.

Pre-asymptotics. Theories are, of course, bad, but they can be worse in some situations when they were derived in idealized situations, the asymptote, but are used outside the asymptote (its limit, say infinity or the infinitesimal). Some asymptotic properties do work well preasymptotically (Mediocristan), which is why casinos do well, but others do not, particularly when it comes to Extremistan.

Most statistical education is based on these asymptotic, Platonic properties—yet we live in the real world that rarely resembles the asymptote. Furthermore, this compounds the ludic fallacy: most of what students of statistics do is assume a structure, typically with a known probability. Yet the problem we have is not so much making computations once you know the probabilities, but finding the true distribution.

The Inverse Problem Of The Rare Events

Let us start with the inverse problem of rare events and proceed with a simple, nonmathematical argument. In August 2007, The Wall Street Journal published a statement by one financial economist, expressing his surprise that financial markets experienced a string of events that “would happen once in 10,000 years”. A portrait of the gentleman accompanying the article revealed that he was considerably  younger than 10,000 years; it is therefore fair to assume that he was not drawing his inference from his own empirical experience (and not from history at large), but from some theoretical model that produces the risk of rare events, or what he perceived to be rare events.

Alas, the rarer the event, the more theory you need (since we don’t observe it). So the rarer the event, the worse its inverse problem. And theories are fragile (just think of Doctor Bernanke).

The tragedy is as follows. Suppose that you are deriving probabilities of future occurrences from the data, assuming (generously) that the past is representative of the future. Now, say that you estimate that an event happens every 1,000 days. You will need a lot more data than 1,000 days to ascertain its frequency, say 3,000 days. Now, what if the event happens once every 5,000 days? The estimation of this probability requires some larger number, 15,000 or more. The smaller the probability, the more observations you need, and the greater the estimation error for a set number of observations. Therefore, to estimate a rare event you need a sample that is larger and larger in inverse proportion to the occurrence of the event.

If small probability events carry large impacts, and (at the same time) these small probability events are more difficult to compute from past data itself, then: our empirical knowledge about the potential contribution—or role—of rare events (probability × consequence) is inversely proportional to their impact. This is why we should worry in the fourth quadrant!

For rare events, the confirmation bias (the tendency, Bernanke-style, of finding samples that confirm your opinion, not those that disconfirm it) is very costly and very distorting. Why? Most of histories of Black Swan prone events is going to be Black Swan free! Most samples will not reveal the black swans—except after if you are hit with them, in which case you will not be in a position to discuss them. Indeed I show with 40 years of data that past Black Swans do not predict future Black Swans in socio-economic life.

Figure 4 The Confirmation Bias At Work. For left-tailed fat-tailed distributions, we do not see much of negative outcomes for surviving entities AND we have a small sample in the left tail. This is why we tend to see a better past for a certain class of time series than warranted.

• Read the full article at Edge.org: THE FOURTH QUADRANT: A MAP OF THE LIMITS OF STATISTICS [9.15.08] By Nassim Nicholas Taleb
• Technical Appendix to “The Fourth Quadrant”— Click Here
• Technical Appendix to “The Fourth Quadrant”— Click Here to read the origina at Edge.org