The Inverse Turkey Problem

THE INVERSE TURKEY PROBLEM

Now some plumbing behind what I am saying—epistemology of statistical statements. The following discussion will show how the unknown, what you don’t see, can contain good news in one case and bad news in another. And in Extremistan territory, things get even more accentuated.

To repeat (it is necessary to repeat because intellectuals tend to forget it), evidence of absence is not absence of evidence, a simple point that has the following implications: for the antifragile, good news tends to be absent from past data, and for the fragile it is the bad news that doesn’t show easily.

Imagine going to Mexico with a notebook and trying to figure out the average wealth of the population from talking to people you randomly encounter. Odds are that, without Carlos Slim in your sample, you have little information. For out of the hundred or so million Mexicans, Slim would (I estimate) be richer than the bottom seventy to ninety million all taken together. So you may sample fifty million persons and unless you include that “rare event,” you may have nothing in your sample and underestimate the total wealth.

Remember the graphs in Figures 6 or 7 illustrating the payoff from trial and error. When engaging in tinkering, you incur a lot of small losses, then once in a while you find something rather significant. Such methodology will show nasty attributes when seen from the outside—it hides its qualities, not its defects.

In the antifragile case (of positive asymmetries, positive Black Swan businesses), such as trial and error, the sample track record will tend to underestimate the long-term average; it will hide the qualities, not the defects.

Recall our mission to “not be a turkey.” The take-home is that, when facing a long sample subjected to turkey problems, one tends to estimate a lower number of adverse events—simply, rare events are rare, and tend not to show up in past samples, and given that the rare events in this negative-asymmetry case are harmful, we get a rosier picture than reality. But here we face the mirror image, the reverse situation. Under positive asymmetries, that is, the antifragile case, the “unseen” is positive. So “empirical evidence” tends to miss positive events and underestimate the total benefits. Figure 35, which is not included here, illustrates the pattern: in a positively skewed (antifragile) time series, the filled area—what we do not tend to see in small samples due to insufficient data points—captures the unseen good stuff, leading to an underestimation of benefits. The same logic applies in reverse for the fragile turkey problem, where the shaded area hides the negative rare events. The more technical sections label these zones ωB (turkey) and ωC (inverse turkey), and notably, the shaded area increases with model error.

As to the classic turkey problem, the rule is as follows.

In the fragile case of negative asymmetries (turkey problems), a sample track record that misses rare losses will overestimate the long-term average payoff; it will hide the defects and display the qualities.

The consequences make life simple. But since standard methodologies do not take asymmetries into account, about anyone who studied conventional statistics without getting very deep into the subject (just to theorize in social science or teach students) will get the turkey problem wrong. I have a simple rule, that those who teach at Harvard should be expected to have much less understanding of things than cab drivers or people innocent of canned methods of inference (it is a heuristic, it can be wrong, but it works; it came to my attention as the Harvard Business School used to include Fragilista Robert C. Merton on its staff).

So let us pick on Harvard Business School professors who deserve it quite a bit. When it comes to the first case (the error of ignoring positive asymmetries), one Harvard Business School professor, Gary Pisano, writing about the potential of biotech, made the elementary inverse-turkey mistake, not realizing that in a business with limited losses and unlimited potential (the exact opposite of banking), what you don’t see can be both significant and hidden from the past. He writes: “Despite the commercial success of several companies and the stunning growth in revenues for the industry as a whole, most biotechnology firms earn no profit.” This may be correct, but the inference from it is wrong, possibly backward, on two counts, and it helps to repeat the logic owing to the gravity of the consequences. First, “most companies” in Extremistan make no profit—the rare event dominates, and a small number of companies generate all the shekels. And whatever point he may have, in the presence of the kind of asymmetry and optionality we see in Figure 7, it is inconclusive, so it is better to write about another subject, something less harmful that may interest Harvard students, like how to make a convincing PowerPoint presentation or the difference in managerial cultures between the Japanese and the French. Again, he may be right about the pitiful potential of biotech investments, but not on the basis of the data he showed.

Now why is such thinking by the likes of Professor Pisano dangerous? It is not a matter of whether or not he would inhibit research in biotech. The problem is that such a mistake inhibits everything in economic life that has antifragile properties (more technically, “right-skewed”). And it would fragilize by favoring matters that are “sure bets.”

Remarkably, another Harvard professor, Kenneth Froot, made the exact same mistake, but in the opposite direction, with the negative asymmetries. Looking at reinsurance companies (those that insure catastrophic events), he thought that he found an aberration. They made too much profit given the risks they took, as catastrophes seemed to occur less often than what was reflected in the premia. He missed the point that catastrophic events hit them only negatively, and tend to be absent from past data (again, they are rare). Remember the turkey problem. One single episode, the asbestos liabilities, bankrupted families of Lloyd underwriters, losing income made over generations. One single episode.

We will return to these two distinct payoffs, with “bounded left” (limited losses, like Thales’ bet) and “bounded right” (limited gains, like insurance or banking). The distinction is crucial, as most payoffs in life fall in either one or the other category.