Finance does not understand the physics of preferential attachment. According to Taleb, the intuitively appealing preferential attachment is incomplete. This is a tragedy for his ‘Black Swan’ because preferential attachment is the other name for ‘Rich Get Richer’. Taleb bases his philosophy of randomness on the non-normal power law behavior which is also another way of looking at ‘Rich Get Richer’ mathematics.
There is not only enough scientific research to prove that assuming power law to be a law of nature is an overstatement but also the researcher behind the recent publications on preferential attachment, Laszlo Barabasi, the author of the popular books ‘Linked’ and ‘Bursts’ is credited for revisiting America i.e. finding something that has already been found first by Herbert Simon in 1955 and then by Günter et al. in 1992. There are other scientific publications which challenge both Barabasi and power law generating mechanisms.
If this was not enough, Barabasi admits that it’s tough to explain why sometimes preferential attachment fails and a second mover like Google overtakes the first mover like Yahoo. He calls it the luck factor. In other words, the ‘Rich’ is supplanted by the ‘Not Rich’ or ‘Poor’ because of luck. This is why the ‘Rich Get Richer’ mathematics of Barabasi and his 150 years of research predecessors is weak. Strangely history of research starting 1880’s with quantitative linguistics has been more focused on ‘Rich Get Richer’ rather than the failure of the phenomenon primarily because there were no computers then. Nobody asked the simple question for 150 years that why do sometimes the rich fail to get richer. Taleb made the same mistake. Instead of focussing on the mathematics, he opted to assume the robustness of his premise.
Taleb’s observation on the incompleteness of the preferential attachment idea is at the heart of his ‘Black Swan’ philosophy. If the preferential attachment is an incomplete science, the power law is an incomplete framework. Using something half cooked to explain the formation of outliers can not be called Science.
The persistence of probability in power law distribution and the fast probability decay in the normal distribution is stating the obvious, which has nothing to do with the creation of outliers. The mechanism which explains the persistence and its failure is real mathematics. It is this mathematics that can also explain why persistence eventually fails. Why do the ‘Poor Get Rich’? How the ‘Rich Get Richer’ is connected to the ‘Poor Get Richer’? There’s no architecture in Taleb’s reasoning. Telling readers to adopt a barbell approach to investing, small weight to a high-risk portion of the portfolio and high weight to a low-risk portion of the portfolio without a durational advice or risk preference background is careless financial advice.
It’s surprising that Taleb uses the height case in his book to explain how normal distribution is flawed. The discoverer of mean reversion, Francis Galton also used a height experiment in his paper “Regression towards mediocrity in hereditary stature” (1886) to back his findings. Taleb’s story based on power law is compelling narrative but without any framework that could explain the process of uncertainty and formation of outliers. Outliers do not emerge out of a vacuum. The system which creates the ‘Rich Get Richer’ is also the same system which creates the ‘Poor Get Richer’. Reversion (normality) and Diversion (non-normality) are part of the same architecture.
However beautiful a hypothesis, it is hard to stand the test of time. The Black Swan idea is rooted in a flawed assumption of Science and an incomplete understanding of history.
This piece was written based on a request made by Taleb in his book for someone to prove him wrong. “Perhaps one day I will be lucky enough to read an attack on this book in a diatribe called The White Swan.”
The book will follow but it’s not called ‘The White Swan’.