Bryan Caplan  

How Kahneman Underestimates Luck

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When I received Kahneman's Thinking: Fast and Slow, I opened to a random page, and found a big error:
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.
Kahneman drastically understates the power of (bad) luck.  Yes, just prior to fertilization, there was a 50/50 chance that Hitler would have been a girl.  But it's also true that just prior to fertilization, there was roughly a 149,999,999 in 300,000,000 chance that a different "male" sperm would have hit the egg.  (There are roughly 300,000,000 sperm per incident, roughly half of them "male"). 

Yes, such a baby would still have been named Adolf Hitler.  But in all likelihood the world never would have heard of him.  A quarter of his DNA would have been different.*  The chance he would have attained Hitler's political prominence would have been near-zero.  If we compound the births of Hitler, Stalin, and Mao, the probability of a twentieth century without any of the three isn't 12.5%; it's (1-1/299,999,999)^3=99.99999901%!

Under hereditary monarchy, Kahneman's calculation might be defensible.  Maybe any male sibling of an infamous king would have been comparably villainous in his stead.  But Hitler, Stalin, and Mao all had humble origins.  They traveled from obscurity to power on hazardous paths.  The chance that a substitute sibling would have made the same journey - and been at all the right places at the right time - is vanishingly small.

Of course, this just confirms Kahneman's deeper point: Human beings underestimate luck - even the great Kahneman himself.
 
* The egg's DNA would have been the same, but two sperm from the same man have only half their DNA in common, so the shared DNA would be 50%+.5*50%=75%.


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COMMENTS (24 to date)
Eric writes:

Yipe!!! The real "luck" has to do with the probablity that the first "order statistic" of Hitler's cohort would be as bad or worse than Hitler. Yes, Hitler's birth was improbable but so were the other, what, 100s of millions in his cohort. It seems very unlikely that something as "improbable" as Hitler/Stalin/Mao would occur in a century if the relevant event (specifically Hitler/Stalin/Mao) were as improbable as you say.
To determine this requires some estimate of the full distribution and, specifically, the tails so the estimates of the first, second and third order statistic could be determined. I expect, given no other information, that a group comparable to Hitler, Stalin and Mao is at about the 50% percentile.

Tahtweasel writes:

Why stop there? Why not include mortality tables, genealogy back to the beginning of time, or Hitler's admission odds to art school? Kahneman was making a simple rhetorical point, but at least it's obvious that his math isn't serious.

Yours isn't either. Obviously, the particular course of history we experienced, relative to all the courses of history that could have happened, was infinitely unlikely.

The existence of Mao and Hitler doesn't prove we were unlucky than the existence of Norman Borlaug and Albert Einstein makes us lucky. You can't just hypothesize about what would happen if you "reroll" the genetic dice on the exceptional people. You have to think about what would happen if you rerolled the dice on everyone else, too - all the middle managers and insurance claims adjusters and accountants and machinists. How many of them could have become heroes or villains with a reroll of the genetic dice?

It's an impossible question to answer.

Dan Carroll writes:

Did Hitler produce Germany, or did Germany produce Hitler? In that time and place, would someone else have stepped into the void, and how would have history been different? Yes, the name might have been different, but how different would the results have been? There have been many crazy people in the world, why did Hitler emerge when he did?

Thus, the probability of these or similar bad events is not quite as small as it might seem.

Jack writes:

I may be wrong, but the I think the statistical interpretation here is not quite right, for reasons detailed in the papers by Hal White and co-authors on data snooping. Basically, the odds of these three murderous dictators is infinitesimal, but the odds of *some* trio of murderous dictators is much greater.

Tribsantos writes:

Bryan,
How do you reconcile your views that natural talent and luck play an enormous role on later outcome in life with your libertarian views that compensation should be almost solely based on performance (and please correct me if I'm not getting your views right).
To me, the more that pure hard work determines your gains, the less redistribution there should be. But if natural talent (which is due to luck) and random events play a big role, doesn't redistribution work as an insurance policy against bad luck?

Steve S writes:

I agree with Dan Carroll.

These three people were in exceptional echelons of power, but without them (or a more timid genetic version of them), would the actions of millions of their followers have changed significantly? Somebody else would have stepped up.

I think we are drastically overestimating the importance of individuals, especially in terms of their contribution to overcoming the inertia to get a revolution/genocide/etc going.

Philo writes:

"[T]wo sperm from the same man have only half their DNA in common . . . ." This is a huge underestimate. Two human beings *taken at random* have something like 98% of their DNA in common; two sperm from the same man will then coincide at least 99%.

A.B. writes:

There could be only one ruler of Germany, you don't observe all the prospective evil rulers who didn't ascend to power because he did.

In your counterfactual, what are the odds that someone just as evil takes power?

I'd say pretty high.

Hitler won the election AND was at the far end of the evil curve. Most people do not win election and those who do are typically not as evil as him.
This makes it very likely that he won the elections *because* he was very evil to begin with.

This brings a side point...

In hereditary monarchy rulers are guaranteed to be roughly average people.

Non hereditary rulership opens the door to extremely strong selections effect. For example a political system might be structured such that the most evil person win.

We should observe the variance of ruler quality to be much lower in hereditary-monarchies.

djf writes:

It is true that each sperm has half of a man's DNA, but it does not follow that each sperm has exactly half its DNA in common with every other sperm. Any two sperm from the same man may have more or less than half their DNA in common. Think about it.

The point stands that, if the mother's egg was fertilized by a different sperm during the same act of coitus, a very different person might very well have resulted.

PrometheeFeu writes:

@Bryan Caplan:

I take the view that Hitler's policy were the product of his time and not the other way around. Or perhaps a bit more accurately, I think that Hitler was able to rise to such prominence because of the policies he supported. Had he not been born, some other evil dictator of comparable evil would most likely have taken the reigns.

I am curious similarly to Tribsantos on how you reconcile your views that people rise in life largely due to chance and heredity with your views that resources go to those who deserve them.

Eric Larson writes:

I agree with Dan Carroll et al. This is a tragic error from an avid reader of Tostoy.

frankcross writes:

This is silly. We have no prior. Perhaps it was bad luck to genetically get Hitler. Perhaps it was good luck to not genetically get ten more. There's no way of knowing, so I'm guessing it was probabilistically realistic

Vangel writes:

Imagine what would have happened if Woodrow Wilson's fertilization had been different? No American entry into WWI. No success by Lenin and Stalin in taking down the Karensky government. No Carthaginian peace. No Hitler. Millions who were killed would have been alive and much less capital would have been destroyed by a needless war.

Bob Murphy writes:

I think this is the first time I have ever encountered a blog post in which every single comment was more insightful than the original post.

Randy writes:

A genetic predisposition for violence is the norm in human beings. For evidence I cite the periodic cycles of mass violence throughout recorded history - and experience. And, no, modern progressive thought has not defeated it - just take a look at an OWS crowd.

Stephen Stanton writes:

Agree with Eric and others... There are billions of chances to get a monster each generation. We are bound to get at least a few.

For every billion-to-one longshot that occurs, by definition there are about a billion others that could have but didn't.

BTW - So many of Chemistry's laws are nothing more than applied statistics on very large populations... When you have 6.02 x10^23 particles, statistical descriptions of their movement become remarkably stable in repeatable experiments (e.g., pressure at a given temperature).

If we could observe the populations of a few quadrillion parallel earths, I suspect we'd see a pretty tight clustering of leadership traits emerge in similar scenarios. (I tend to buy the theory that "The times chose a Hitler, He didn't create the times.")

justin writes:

There was a 50/50 chance Hitler could've been a girl. There's also a chance that there was a girl in the 1940's who at one point had a 50/50 chance of becoming a boy who would one day to Hitler-esque things, so I'd have to think the two effects would balance out on average.

chris fisher writes:

@Philo
I have twins with the same DNA, they have very different personalities. DNA may contribute but it does not determine.

@Caplan
I think, as other commenters are saying, you are forgeting the law of large numbers. If Hitler had a 1 in a billion chance of happening, the world does have 7 billion people.

Mike Rulle writes:

I am truly shocked at Brian's take. Being familiar with Kahneman's interesting but overrated work, I assumed he would point out the absurdity of applying probability to the issue of 20th century dictators, not his bad statistics. Yes, at the micro-level, the odds that this "Mike Rulle" would exist versus sperm number 653,000 is fascinating to contemplate philosophically. But what does it have to do with anything? Every single thing at the quantum level and above is subject to the same "analysis" of randomness. But everything is so random it begins looking like determinism. We have what we have and the counterfactuals do not and can never exist.

But my point on Kahneman is not his truly bad statistics, but his even more absurd sense of history. He takes as a given everything that did exist (duh) and then imagines the counterfactual on the margin of 3 guys not existing. Has he read any history? Their were dozens vying for Hitlers position with effectively the same views. Hitler simply believed he was better and persuaded others he was. Of course it would have
been "different" had someone else led Germany. But it is far more plausible to imagine some other guy, say Ernst Rohm, would have taken over than it is to imagine there would have been no WWII without Hitler.

But I hate to even debate at this level. We all exist now, not sperm number 653,000, or whatever. Randomness is both ever present and irrelevant,, at least at the level of analysis Bryan got sucked into by Kahneman's lazy statistics. While fun the first 3 or 4 times one thinks of these issues, it has nothing to do with decisions we need to make constantly in all aspects of our lives.

Matthew Gunn writes:

Rerun the 20th century several times and the chance of peace and tranquility won't be 99.999%. Sure, the chance of this exact Hitler, Stalin, and Mao combination may have probability measure approaching zero but so what? It's rather irrelevant. What we care about is a much broader set of events! For example, what's the probability of millions of people getting killed in war? What's the probability of a genocidal leader rising to power in Europe?

Complaining about our bad luck for having Hitler, Stalin and Mao in the 20th century sounds a bit like a poker player wailing about how incredibly unlucky he was to get beaten by a player holding a 8 and 10 of spades when the flop came out with a 7 9 and the river was a 6 for a straight. Sure, the exact way our player got beaten was incredibly unlikely, but the unconditional probability of him losing ex-ante was rather close to 50%.

In short, saying a *very specific event* has a probability of near zero actually doesn't mean much of anything.

Thomas Sewell writes:

Seems like we all have essentially the same point, so I won't belabor it.

I will take it one step further. It's possible we were lucky to get Hitler, genetically-speaking.

What if he wasn't there, but someone else who was just as evil, but slightly less capable of an organizer, ran things in Germany instead. So far so good, but what if that replacement person wasn't as credulous and superstitious and paranoid as Hitler? What if they were more effective in running Germany during WW II, like several German general officers Hitler killed would have been?

The allies might not have even won... the replacement for Hitler might have conquered Britain and been satisfied with an alliance with Stalin.

It's very, very hard to make a case that you can tweak one thing in history and then predict that stuff will actually turn out better.

mark writes:

Agree with the other commenters that this overstates the role of luck. It's just selective hindsight -- that moment did not determine anything. It may have increased the potential for one large set of outcomes over others by some microscopic amount but it's absurd to connect that one small event with its extreme consequences, as if there was some cause snd effect.

James A Donald writes:

Comes the hour, comes the man.

If a time traveler strangled Stalin, Hitler, and Mao in their cradles, things would have turned out much the same. In the case of Stalin, probably a great deal worse.

In Stalin's pamphlet "Dizzy with success" it looks to me he was trying to thwart the terror, but terrified that if he tried to thwart it too vigorously, would be its next victim.

The French Red Terror, the Soviet Great Terror, the Cambodian autogenocide, and many others are all examples of what I call left political singularities.

Under Tsar Nicholas II, the way to power came to be to be lefter than thou. The safest way to ally was no enemies to the left, no friends to the right. And so everything from there on moved ever lefter. And the lefter things got, the more the way to power was to be lefter than thou, the more dangerous it became to have friends to the right, so the lefter things became, the faster they moved left, consuming each leader in turn for insufficient leftism.

Left wing repression tends to make things lefter, which tends to worsen left wing repression.

Right wing repression does not have this effect, because right wing repression tends to hold things the same, or return to a real or imagined recent past, and because there is no right. The right is the non left. The right is a coalition of whosoever disagrees with any one of a thousand points of left wing doctrine.

Gene Callahan writes:

"We have what we have and the counterfactuals do not and can never exist."

Thank you, Mike! The concept of odds applied to what has actually transpired is the problem: it is nonsense.

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