Wherein I Correct Nobel Laureate Daniel Kahneman’s Math

The Hitlers and Stalins We Never Knew
Beware of mathematically grounded assertions that omit one side of the equation.
Bloomberg, October 10, 2014




I am a fan of Morgan Housel, columnist at the Motley Fool. His writings evince a strong understanding of behavioral issues, and he has a gift of sifting through the nonsense to get to what really matters. Only on rare occasions do I get to disagree with him.

Today is one of those times.

Housel has been sporadically posting notes on books he has read. This week, he discussed “6 Things I Learned From the book ‘Thinking Fast and Slow,'” by Princeton psychologist Daniel Kahneman.

Most of the column is solid, with five interesting bullet points. But one of Kahneman’s points leapt out at me as having a small math error: The most important things in life are unpredictable:

The idea that large historical events are determined by luck is profoundly shocking, although it is demonstrably true. It is hard to think of the history of the twentieth century, including its large social movements, without bringing in the role of Hitler, Stalin, and Mao Zedong.

But there was a moment in time, just before an egg was fertilized, when there was a fifty-fifty chance that the embryo that became Hitler could have been a female. Compounding the three events, there was a probability of one-eighth of a twentieth century without any of the three great villains and it is impossible to argue that history would have been roughly the same in their absence. The fertilization of these three eggs had momentous consequences, and it makes a joke of the idea that long-term developments are predictable.

I have no problem with the random aspect of history — yes, many important things in life are unpredictable. The problem with this analysis is that it is mathematically one-sided. As is so often the case, the counterfactual provides insight.

Obviously, Hitler, Stalin, and Mao were male, a prerequisite for global chaos and mass murder. And it is true that had any or all of these three villains been born female, the course of the 20th century would have been very different.

However, that outcome is only half of the potential outcomes, Statistically, it is just as likely that there were potential villains who did no damage to humanity because the 50/50 (really, more like 51/49) chance of them being male came up negative.

In other words, how many other evil villains didn’t cause bloodshed and war or kill tens of millions of people by dint of not having that Y chromosome?

What we end up with is a biased sample set. We don’t see the outcomes that did little harm. (See Peter Orzag’s reviewof Jordan Ellenberg’s “How Not to Be Wrong: The Power of Mathematical Thinking.”)

Over the 20th century, out of billions and billions of people, a small handful were destructive despots who changed the course of human history.

We don’t know about these other “great villains” because of the random roll of the chromosome dice that came up XX instead of XY. The female versions of these villains — Hitler-XX, Stalin-XX, Mao-XX and no one knows how countless others — all had the same potential for wreaking havoc, but by dint of that chance outcome of being a female, were never able to do that much damage.

I don’t want to understate the role of randomness in outcomes — we know it is tremendous. However, it is important to be aware of the biased sample sets we unwittingly use all the time. The odds suggest that for every blood thirsty lunatic who became a tyrant by virtue of that XY chromosome, there is likely another tyrant who never did much harm because of the XX outcome.

I admire Kahneman’s work, and I very much am on board with his understanding of the many cognitive errors that interfere with our understanding of the world around us.

I feel compelled to point out that he is only presenting half of the picture regarding the impact of randomness on outcomes. Sometimes chance works in our favor while other times it works against us. But it is most definitely in our interest to understand both sides of that equation.



I originally published this at Bloomberg, October 10, 2014. All of my Bloomberg columns can be found here and here



Print Friendly, PDF & Email

What's been said:

Discussions found on the web:

Posted Under