Predicting BIG

 

As a continuation of the Olympic-sized meme and my blog from last week (“Pathologies in our Decision-Making”), I want to explore the notion that large populations are easier to predict than smaller ones. I first became aware of this idea as a boy, when I was reading Isaac Asimov’s Foundation trilogy. For those of you who are unaware of this classic of science fiction, in a future Milky Way Galaxy mankind has spread throughout, and an inter-stellar government of sorts is set up on the planet Trantor. One Hari Seldon invents a way of calculating how future events will unfold, and names it the Risk Management Special Interest Group from PMI®. No, just kidding. He names it “Psychohistory,” and, as one might imagine, many people are very interested in what Hari and his associates “know” is going to happen in the future.

Now, the way Psychohistory’s mathematical processes are (barely) described, one could not possibly predict the behavior of a single gas molecule. But, get a bunch of them together in a container, and suddenly their behavior becomes quite predictable. Since, at this point in the future, the number of humans in the galaxy is in the trillions, the macro-future can be calculated, even if the micro-future can’t be known with certainty.

One of the fascinating (and intellectually honest) things about the Foundation Trilogy is how the Seldon Plan is undone. A mutant arises, one who can telepathically change people’s minds. He quickly rises to power, and very nearly destroys the entire basis for inter-stellar civilization. The reason Psychohistory could not be used to see his rise to power coming is because he was a mutant, and such mutations were outside the model that Psychohistory used.

Certainly one of the drivers behind this bigger-is-easier-to-predict bizarro-world narrative lies with the notions of the statisticians, who attempt to use their data to calculate the odds of future events actually occurring. Small sample sizes, you see, are given to large variances. The larger the sample size, generally speaking, the more it assumes the familiar shape of the Bell Curve, should it be graphically represented. So, if some statistician were to, say, use the tools of statistics and probability to predict the outcome of this November’s presidential election, it just won’t do to ask a few dozen people at the campus of the University of California, Berkley, whom they would vote for (actually, the University of California anywhere). Our statistician would simply have to throw in an occasional meat-eating church-goer, if he wanted an accurate prediction.

But even with a good sample, there are (at least) two major problems with predicting the future based on data that captures past behaviors: the limiting effects of mathematical models, and network theory.

Notice how Psychohistory was undone because of an event that occurred that was outside of its model. Any attempt to limit possible behaviors, strategies, or tactics from any given population is extremely vulnerable to occurrences of the highly improbable, as Nassim Taleb describes brilliantly in his book The Black Swan, the Impact of the HIGHLY IMPROBABLE (Random House, 2007). But what about the notion that the sheer size of the sample somehow mitigates the impact of highly improbable (i.e., ”outliers”) events? This butts up against network theory, and Metcalfe’s Law.

As I insightfully discuss in my recently-released, must-have book Game Theory In Management, Metcalfe’s Law shows that while, say, two telephones have one connection between them, six phones have 15. In other words, the larger the network, the more powerful it is. Ironically, the larger networks become, the more susceptible they are to cascading events, also known as the Butterfly Effect, stated colloquially as “if a butterfly flaps its wings in Brazil, does that cause a hurricane in Texas?” Put another way, seemingly small variations in few (or singular) nodes in a large network can have catastrophic effects on a large number of nodes that are nominally far away, or non-intuitively connected. In other words, the larger the sample size (or network), the more difficult it is to predict its behavior, even regarding cataclysmic events.

Essentially, the only way the risk management aficionados can assert any calculated insight into the unfolding of future events is if they (conveniently) ignore both Black Swan theory and Metcalf’s Law, and hope that no one in their epistemological snake-oil audience knows about them.

Or have read this blog.