I’m reading Daniel Kahneman’s Thinking, Fast and Slow, and I wasn’t quite satisfied by the author’s presentation of the “Librarian or Farmer” question (pp. 6-7 of the 2013 paperback).
As you consider the next question, please assume that Steve was selected at random from a representative sample. An individual has been described by a neighbor as follows: “Steve is very shy and withdrawn, invariably helpful but with little interest in people or in the world of reality. A meek and tidy soul, he has a need for order and structure, and a passion for detail.” Is Steve more likely to be a librarian or a farmer?
According to Kahneman, most people assume Steve is a librarian. That answer is wrong, because it depends on occupational stereotypes while ignoring “equally relevant statistical considerations.” The question is supposed to illustrate the shallowness of our intuitions about probability. “Did it occur to you that there are more than 20 male farmers for each male librarian in the United States? Because there are so many more farmers, it is almost certain that more ‘meek and tidy’ souls will be found on tractors than at library information desks.”
But the question itself is unclear: we are not told what “representative sample” Steve was selected from. Kahneman’s discussion of the “correct” answer suggests that he’s thinking of a representative sample of males throughout the United States, so let’s assume that. Now, to arrive at Kahneman’s correct answer we should reason as follows: Yes, it might be true that the proportion of shy individuals among male librarians is larger than the proportion of shy individuals among male farmers, but when we look at the U.S. population as a whole, the proportion of shy librarians among all U.S. males is in fact smaller than the proportion of shy farmers among all U.S. males. Choosing at random from U.S. males, we’re more likely to get a shy farmer because the “base rate” of farmers is so much higher.
I would argue that this “correct” answer is wrong if we consider the other significant details in the question, even assuming a 20:1 ratio of male farmers to librarians.
We’ve been told much more about Steve than that he’s shy. Shyness as a character trait is perfectly consistent with farming: you can be a shy farmer without having your disposition fundamentally challenged. But we’ve been told that Steve “has little interest in the world of reality,” which is quite different from being shy: it’s an extreme attitude that’s in direct conflict with the demands of farming, dependent as that profession is on the reality of weather, seasons, crops, and markets. A farmer with little interest in the world of reality wouldn’t survive long in the job (at least not without an attitude adjustment) while a librarian might do just fine (as long as he has enough tolerance for reality to handle book requests).
The question also gives us information about Steve’s neighbor: we get to hear how the neighbor speaks, and if we’re trying to make the very best guess we can, this linguistic information should figure into our thinking. If Steve’s neighbor speaks like a farmer, this increases the chance that Steve is a farmer too, since farmers tend to live in rural areas where there isn’t a big mix of professions. If Steve’s neighbor has a more urban style of speech, this suggests that they both live in a town or city where Steve is more likely to work indoors. So let’s listen to Steve’s neighbor. A phrase such as “A meek and tidy soul, he has a need for order and structure, and a passion for detail” sounds like it was uttered by a psychologist or an author writing a character synopsis. We might expect that a real farmer describing another farmer would speak in a more vernacular style, and with more concreteness; instead of citing an abstract “passion for detail,” he might talk about how the other farmer cares for each seed he plants. I’m not a farmer myself, and I don’t want to be too stereotypical in my assumptions about dialect, but I’m pretty sure that what’s quoted there isn’t farm talk.
Let’s say that Property X means “being someone with little interest in the world of reality, whose neighbor would describe you with the exact words ‘a meek and tidy soul’”. Now even if the proportion of shy librarians among all U.S. males is smaller than the proportion of shy farmers among all U.S. males, I’m willing to bet that the proportion of Property X librarians among all U.S. males is larger than the proportion of Property X farmers among all U.S. males.
You could say I’m reading too much into the question, or that my reasoning is more elaborate than what happens in most people’s minds when they jump to the conclusion that Steve is a librarian. I would argue that my reasoning is not unusual at all. What might be unusual is the act of voicing it in such detail, but I think the sorts of inferences I’ve described here go on in people’s minds without their even being aware of it. Kahneman treats the Librarian or Farmer question as an example of the shallowness of our statistical intuitions because it shows that most people don’t consider base rates, and yet he ignores the possibility that our intuitions might depend on other important considerations which trump the base rate discrepancy: in this case, our intuitions might rely on a distinction between temperament (shyness) and an actively held attitude (disinterest in reality), an understanding of the link between attitude and profession (it’s hard to farm if you don’t care about reality), an understanding of speaking style and its implications (farmers tend to speak differently from city dwellers), and an understanding of neighbor relationships and geography (farmers tend to live near other farmers). I don’t disagree with Kahneman’s overall point, which is that people’s statistical intuitions are often shallow, but this may be one case where the shallowness is less in the intuition than in how the psychologist analyzes it.