Thinking, Fast and Slow. 10 The Law of Small Numbers

Following the schedule of our Reading Calendar

Our automatic System 1, we know, is a genius of mathematics when complicated calculations have to be performed in order, for instance, to catch a ball thrown to us at high speed. However, this chapter is devoted to explain to us and convince us that this very System 1 is an extraordinary lousy statistician. Statistics works with probabilities of things that may happen or not and keeps at play simultaneously a lot of different options that could eventually materialize. This is something our System 1 is not prepared to work with. He needs certainty, simplicity and a chain of causalities that makes sense of the events that he perceives around him.

We are introduced to this idea by using what the author calls the “law of small numbers”. This is simply the fact that small samples generate a higher frequency of extreme observations that larger ones. Easy, right? Then we begin the chapter confronted to some observations in the incidence of kidney cancer in the US. And that allows us to notice how difficult is to use in practice that knowledge (the law of small numbers) that we all understand in theory. This is Kahneman’s favorite strategy: begin the chapter reducing the self esteem of the reader to make them more attentive at the subsequent discussion.

There are to cognitive biases presented to us in the chapter. One of them says that we are always much more interested in knowing facts that in assessing the reliability of those facts. Assigning reliabilities imply to assign degrees of reality to the facts that we know. System 1 can not cope with that. For him, events happen or doesn’t happen. No blurred logic here.

The second is our deep incapability to recognize randomness. In front of randomness we see patterns and clusters. We look for causal explanations in everything although most of what happens is just random. We are “fooled by randomness”. This is all very Talebian.

To understand this two biases is of tantamount importance in order to understand the limitations of our cognitive systems. To be able to develop mechanisms two fight them in practice and to be conscious of their presence when we are falling into them looks to me as an Herculean task. I am really curious to know if this book, beyond its theoretical description of human cognitive weaknesses, will be able to provide any kind of help.

2 thoughts on “Thinking, Fast and Slow. 10 The Law of Small Numbers

  1. This is a very important chapter. I use the example of the kidney cancer in class and year after year nobody in the class is able to realize that the reason that both higher incidence and lower incidence of cancer is because we are using a very small group of people. Instead, all the students try to imagine some sort of causal explanation.
    We can’t help but trying to find a cause for anything that happens, and once we build one, we believe it blindly.

  2. Pingback: Chaos, Confusion, Corona, & Covid-19: Farr’s Law of Small Numbers | Fred Lybrand

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