Black Swan Ideas (3)

Joe Firestone’s Blog on Knowledge and Knowledge Management


Lottery Ticket and Ludic Fallacies, Mandelbrodtian Randomness, Gray Swans, and the Narrative Fallacy

June 2nd, 2009

More on ideas from Nassim Nicholas Taleb’s (NNT) The Black Swan today, including discussions of the Lottery Ticket and Ludic fallacies, Mandelbrodtian Randomness, and Gray Swans, and the Narrative Fallacy.

The Lottery Ticket Fallacy. One of the things NNT calls attention to is the possibility and advisability of living one’s life in such a way that one collects positive Black Swan opportunities. However, this is not so easily done because of the tendency to mistake positive Black Swan opportunities for opportunities that can only produce positive results in a manner consistent with Gaussian normality. The lottery ticket fallacy is a specific form of this error in which the accumulation of opportunities to win the lottery through the accumulation of lottery tickets is taken for the accumulation of positive Black Swan opportunities.

The Ludic Fallacy. This is the idea of associating chance, randomness, and uncertainty in the real world with games of chance and the mathematical models that govern our expectations about them. According to NNT, gambling is “sterilized and domesticated uncertainty.” It is uncertainty in which you know both the rules generating uncertainty and the sources of uncertainty. “In real life you do not know the odds; you need to discover them, and the sources of uncertainty are not defined.” So, according to NNT, mathematizations based on games of chance such as Gaussian Models cannot be applied to the real world of social events and processes, without committing an error. Such models simply don’t work in reality and we risk costly errors if we assume that they can, and apply them in action. NNT illustrates the Ludic fallacy by discussing the risk management efforts of a Las Vegas casino. (pp. 126-130) The casino used sophisticated models and computer systems to protect itself from occasional very lucky people and also from “cheaters.” But it failed to anticipate four key Black Swan events having nothing to do with its models that cost it dearly. In sum, its off-model Black Swans swamped its “on-model risks by a factor of close to 1,000 to 1.”

Mandelbrodtian Randomness and Gray Swans.  Remember that NNT views randomness: “as incomplete information: simply what I cannot guess is random because my knowledge about the causes is incomplete, not necessarily because the process has truly unpredictable properties.” (p. 308) Thus, he views events that do not fit Gaussian models, or deterministic models, as random. Now, within this “random” category, there are events that we have no models for. These are the true Black Swans. But we can get insight, sometimes quite considerable insight, into some occurrences by applying Mandelbrodt’s fractal models, and NNT did this very frequently in his own empirical work. He calls such events “Gray Swans,” because applying fractal models can make some otherwise Black Swans ”appear possible. So to speak, to make us aware of their consequences, to make them gray.” Gray Swans are not entirely predictable because the exponents and “crossover” points in fractal models are difficult to estimate precisely. But they are still very useful, because they provide greater insight into the possible, and allow us to prepare for and either hedge against its occurrence or take advantage of it, if it is a positive “Gray Swan.”

The Narrative Fallacy. This refers to the idea that there is a human need to make sense of, or interpret events we observe, experience, or learn about, as part of a narrative that distinguishes cause and effect, and that can provide us with a strong impression that we understand a sequence of events that has occurred. NNT states that there is a biological basis to our need for narrative. This reflects the increasingly common view that humans are storytelling animals, a staple of Knowledge Management. The danger, or potential fallacy, in imposing narratives on events, according to NNT, arises out of our need to believe that we really do understand a sequence, and to refrain from thinking of counter-narratives, or considering such narratives seriously when we encounter them. In effect, we “platonify” our stories, theories or models. NNT sees the danger of this in a variety of situations in which we are presented with unexplained events, including the practice of data mining, which easily affords us the opportunity to impose narratives on data patterns after the fact. The remedy for the narrative fallacy, NNT thinks, is to make conjectures, perform experiments, and make predictions.

We can see that some of these additional ideas from the Black Swan, like previous ones we have examined, are about the need to be skeptical about our mental models, theories, and assumptions. The Lottery Ticket Fallacy involves thinking that we are dealing with Black Swans, when in fact we are dealing with classical Gaussian randomness. The Ludic Fallacy makes the opposite error of assuming events are Gaussian. when in fact Black Swans are good possibilities. The Narrative Fallacy, identifies a general tendency to make errors in our biological need to create narratives and then be reluctant to think of, or consider, alternatives.

Finally, Mandelbrodtian Randomness enriches NNT’s conceptual scheme, by introducing a third category of fractal models. This both creates additional error possibilities in our assumptions, and also increases the richness of the narratives we can use in describing events. In my next KM blog, I’ll discuss some more of Taleb’s ideas.