Sailer is wrong on Kahneman and probability

In the past, Steve Sailer had done a superb job taking the overrated Malcolm Gladwell down a notch or two. More recently, he’s been aiming his salvos at Daniel Kahneman of the Thinking, Fast and Slow — and of course, Nobel — fame.

Sailer:

Kahneman’s most celebrated shtick is to ask questions that are stupider than people expect him to ask, so they interpret them in a more intelligent fashion than they literally are, and then he says, “Gotcha! I wasn’t asking about the per capita murder rate like you assumed I must be, I was asking a dumber question than that. Burn on you!”

In other words, another wiley Jew is deceiving trusting gentiles with his shtick. How on earth could the notorious Judeophile Sailer stumble upon a pungent trope like that?

There’s also some sniping at the academia in general: “it’s people assuming that the professors wouldn’t be wasting their time with a lot of contrived details simply in order to play a lowbrow trick on them”. In some cases, the criticism is justified. Consider the example of Jack. Perhaps Sailer (or much of his audience) lacks the language to make this precise, so I will. This is a textbook example of confusion between marginal (a priori) probability and conditional probability. If I don’t know anything about Jack, his probability of being an engineer is 30%. As I learn more and more engineery things about him, the probability of him being an engineer conditioned on this additional knowledge increases. I fully agree with Sailer that by providing this additional information, Kahneman and Tversky intentionally prodded the subject toward the latter. [Of course, I would’ve smelled a rat. The only thing we are given hard numbers for is the proportion of engineers; we don’t know anything about the joint distribution of the other engineery properties. For example, it might be the case that everyone in the group satisfies Jack’s engineery description — and then the additional knowledge doesn’t change Jack’s conditional probability of being an engineer at all. This lack of additional quantitative information would have forced me to grudgingly choose the “correct” answer.]

In other cases, Sailer is completely off. A case in point is the “conjunction fallacy,” illustrated by the story of Linda. “Linda is thirty-one years old, single, outspoken, and very bright […] She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations.” Question: “Which alternative is more probable? (1) Linda is a bank teller. (2) Linda is a bank teller and is active in the feminist movement.” Sorry Steve, no matter what philosophical approach to probability you happen to subscribe to, it is never the case that the probability of A and B is greater than the probability of A. I think that the conjunction fallacy is completely real, and is simply yet another illustration (out of many) of how ill-suited untrained human intuition is for probability.

We close on a note of J’accuse.

Everybody was amazed to discover from Kahneman that undergrads fall for a bunch of gags that were surefire ways to fool folks in vaudeville days. Why? Because when Dr. Kahneman tells a story contrived to pull the rug out from under psych majors, it is Science.

This passage prompted me to go ahead order the book. Actually, I didn’t have to; it’s right there in the Introduction (use Amazon’s “look inside” option):

We prepared a survey that included realistic scenarios of statistical issues that arise in research. Amos (Tversky) collected the responses of a group of expert participants in a meeting of the Society of Mathematical Psychology, including the authors of two statistical textbooks. As expected, we found that our expert colleagues, like us, greatly exaggerated the likelihood that the original result of an experiment would be successfully replicated even with a small sample. They also gave very poor advice to a fictitious graduate student about the number of observations she needed to collect. Even statisticians were not good intuitive statisticians.

So Sailer’s characterization of Kahneman and Tversky’s research as “undergrads fall for a bunch of gags” is scandalously, libelously wrong. Such gross misrepresentation is out of character for the normally factually careful Steve Sailer; I expect him to retract that claim and issue a correction.

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9 thoughts on “Sailer is wrong on Kahneman and probability

  1. The point still stands. When people tell you a story with details, one is rational in assuming they are relevant, because usually they are. In real life people aren’t testing your deductive logic very often. It’s a good point, and I have never read an economist make that criticism. So, good for Steve.

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  2. There seems to be typo in your text. You write, “it is never the case that the probability of A and B is greater than the probability of A”. But the question is about probability of A vs that of B, not A+B vs B.

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  3. Yes, Pr[A and B] <= Pr[A]. Blame the imprecision of language, but it's not _irrational_ to assume that the what's really being asked–what with our fuzzy meatbag language and all–is Pr[A and ~B] vs Pr[A and B].

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