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comment by Said Achmiz (SaidAchmiz)
· score: 23 (6 votes) · LW
(I imagine this comment properly belongs here on Less Wrong, when the new versions are posted here; perhaps the mods can move it, then. For now, posting it here because I can’t find a better place for it.)
From the introduction to Map and Territory, section “Noticing Bias”:
Imagine meeting someone for the first time, and knowing nothing about them except that they’re shy.
Question: Is it more likely that this person is a librarian, or a salesperson?
Most people answer “librarian.” Which is a mistake: shy salespeople are much more common than shy librarians, because salespeople in general are much more common than librarians—seventy-five times as common, in the United States.
This is base rate neglect: grounding one’s judgments in how well sets of characteristics feel like they fit together, and neglecting how common each characteristic is in the population at large.
Reading this, I immediately noticed that integrating base rates is not sufficient to make the “librarian” answer a mistake; and therefore we cannot conclude that the reason why people answer thus, is base rate neglect.
In fact, the text does not establish that answering “librarian” is wrong. Consider the claims:
“salespeople in general are much more common than librarians—seventy-five times as common, in the United States”
“shy salespeople are much more common than shy librarians”
The first claim is specific—we’re given a figure (“seventy-five times as common”)—and referenced. (The first footnote cites Weiten, Psychology: Themes and Variations, Briefer Version, Eighth Edition, 2010.) The second claim is neither quantified nor cited. Hmm.
But this is basic Bayes: in order to conclude #2 from #1, we also need another claim, call it #3: that observing that someone is shy does not provide strong enough evidence to overcome our prior probability distribution over a randomly selected person’s profession, and shift our posterior estimate such that “librarian” becomes more likely than “salesperson”. This claim can easily be false—namely, in the case that the proportion of librarians who are shy is at least seventy-five times greater than the proportion of salespeople who are shy.
If claim #3 is false, then answering “librarian” is correct! But also, even if claim #3 is true, then the error of someone answering “librarian” may be simply mis-estimating the relative rates of shyness among salespeople and librarians—which would not be an example of the base rate fallacy.
The text does not comment on this. Perhaps it is assumed that librarians aren’t shy at a rate 75 times greater than salespeople are. (But this is already a pedagogical flaw! And it ignores my second point in the paragraph above…) But is it true? From the provided information, we don’t know.
Note that my criticism of the text of M&T stands regardless of what the facts of the matter are—even if claim #3 is true, the text is, as I say above, quite flawed. Nevertheless, I was curious, and got my hands on a copy of Weiten 2010. The relevant bit is on page 270:
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. Do you think Steve is a salesperson or a librarian? (Adapted from Tversky & Kahneman, 1974, p. 1124)
Using the representativeness heuristic, participants tend to guess that Steve is a librarian because he resembles their prototype of a librarian (Tversky & Kahneman, 1982). In reality, this is not a very wise guess, because it ignores the base rates of librarians and salespeople in the population. Virtually everyone knows that salespeople outnumber librarians by a wide margin (roughly 75 to 1 in the United States). This fact makes it much more likely that Steve is in sales. But in estimating probabilities, people often ignore information on base rates.
(The book does not discuss this particular matter further, though it goes on to further discussion of base rate neglect.)
Note that the “75 to 1” figure, in particular, does not appear to be referenced; nor is there any discussion of the relative rates of shyness among salespeople and librarians. There also does not seem to be any discussion of the possibility, in general, that people are taking base rates into account but mis-estimating the strength of the evidence (though I read only that one section, and not the entire 750-page textbook, so perhaps I missed it).
The two in-text citations in the above quote refer to:
Tversky, A., & Kahneman, D. (1974). Judgments under uncertainty: Heuristics and biases. Science, 185, 1124–1131.
Tversky, A., & Kahneman, D. (1982). Judgment under uncertainty: Heuristics and biases. In D. Kahneman, P. Slovic, & A. Tversky (Eds.), Judgment under uncertainty: Heuristics and biases. New York: Cambridge University Press.
The first source (Tversky & Kahneman, 1974—a paper) contains no mention or discussion of the relative numbers of salespeople and librarians in the general population (and, in fact, describes an experiment where the base rates involved were not base rates in the general population, but rather base rates in an artificially constructed set, making the applicability questionable), nor of their relative rates of shyness.
In the second source (Tversky & Kahneman, 1982—a book), the relevant bit (on page 4) seems to be almost verbatim identical, with minor editing, to the first source. There is no additional information on any of the above topics.
So, tracing back the citations in Map and Territory, we seem to find no good basis at all for a strong conclusion that people who are asked the “salesperson vs. librarian” question ignore base rates; nor for rejecting the possibility that people merely mis-estimate relative rates of shyness among salespeople vs. librarians; nor any information on what those relative rates are; nor for the claim that “most” (or even “many”!) people answer in the alleged way; nor even for the claim that answering “librarian” is a mistake at all…!
I decided to check whether even the “75 to 1 salesperson:librarian ratio” claim is true (remember, said claim in Weiten 2010 is not sourced at all).
The U.S. Bureau of Labor Statistics seems to claim that there are approximately 138,200 librarians in the United States. The American Library Association gives the number as 166,164. (Differences in sources, definitions, and periods of measurement likely explain the discrepancy.)
Bureau of Labor Statistics figures show 14,522,580 as the number of employees in “Sales and Related Occupations”—though this includes many jobs, like “Cashier”, which do not seem to fit the intuitive definition of “salesperson” in the way relevant to the “shyness” question above.
Ignoring that quibble, and taking the average of the two figures above for number of librarians, yields a 96:1 salesperson:librarian ratio in the United States, which is less than an order of magnitude off from the 75:1 figure quoted in Weiten 2010—which difference may be caused by the passage of time. In any case, I think we can call this one factoid more or less confirmed.