Are stereotypes ever irrational?

Harvard’s undergraduate admission office will tell you “There is no typical Harvard student.” This platitude ticks me off. Of course there’s such a thing as a typical Harvard student! Harvard students aren’t magically exceptions to the laws of probability. Just as a robin is a more typical bird than an ostrich, some Harvard students are especially typical. Let’s say (I’m not actually looking at data here) that most Harvard students are rich, most have high SAT scores, most are white, and most are snobbish. Note: I am not a Harvard student. :)

Now, a very typical Harvard student would be rich AND white AND smart AND snobbish. But observe that a given student has a smaller probability of being all of these than of just, say, being rich. If you add enough majority characteristics, eventually the “typical” student will become very rare. Even if there’s a 99% probability of having any one of these characteristics, 0.99n ->0 as n goes to infinity. Some Harvard students are typical; but extremely typical Harvard students are rare. If you encountered a random Harvard student, and expected her to have all the majority characteristics of Harvard students, you could very well be wrong.

So far, so obvious. But who would make that mistake?

You, that’s who. The conjunction fallacy is the tendency of humans to think specific conditions are more probable than general conditions. People are more likely to believe that a smart, single, politically active woman is a feminist bank teller than just a bank teller. Policy experts (in the 1980′s) were more likely to think that the USSR would invade Poland and that the US would break off relations with the USSR, than either one of these events alone. Of course, this is mistaken: the probability of A and B is always less than or equal to the probability of A alone. The reason we make this mistake is the representativeness heuristic: a specific, compelling story that resembles available data is judged as more probable than general (but more likely) data. Judging by this evidence, I’d hypothesize that most people will overestimate the probability of a random Harvard student matching the profile of a “very typical” Harvard student. The conjunction fallacy says something even stronger: the more information you add to the profile of the “very typical” Harvard student, the more specific the portrait you paint (add a popped collar, for instance) the more likely people will think it is. Even though in fact the “typical student” is getting less and less likely as you add more information.

Now, let’s talk about stereotypes. Stereotypes—at least the kind that offend some people—have their apologists. Some people say, “They’re offensive because they’re true. Of course some traits are more common in some populations than others. That’s just having accurate priors.” This is worth taking seriously. The mere act of making assumptions based on statistics is not irrational. In fact, that’s the only way we can go about our daily lives; we make estimates based on what we think is likely. There’s nothing wrong with stating “Most birds can fly,” even if some can’t. And exhortations not to stereotype people are often blatantly irrational. “There is no typical Harvard student”—well, yes, there is. “You can’t make assumptions about people”—well, yes, you can, and you’d be pathologically helpless if you never made any. You can assume people don’t like rotten meat, for instance. If stereotyping is just making inferences, then stereotyping is not just morally acceptable, it’s absolutely necessary. And, though it may be true that some people are offended by some accurate priors and rational inferences, it is not generally good for people to be thus offended; any more than it is good for people to want to be wrong about anything.

But there is a kind of “stereotyping” that really is a logical fallacy. The picture of the “very typical” Harvard student is a stereotype. If people overestimate the probability of that representative-looking picture, then they are stereotyping Harvard students in an irrational way. An irrational stereotype is a “typical” or “representative” picture that isn’t actually all that common. Because the human mind likes stories, because we like completing patterns, we’ll think it’s more likely that someone matches a pattern or story completely than that she matches only part of the story.

There’s a line in the movie Annie Hall that illustrates this. (This is within five minutes of Alvy meeting Allison.)

Alvy Singer: You, you, you’re like New York, Jewish, left-wing, liberal, intellectual, Central Park West, Brandeis University, the socialist summer camps and the, the father with the Ben Shahn drawings, right, and the really, y’know, strike-oriented kind of, red diaper, stop me before I make a complete imbecile of myself.

Allison: No, that was wonderful. I love being reduced to a cultural stereotype.

If Alvy had only stopped with “New York, Jewish, left-wing,” he’d probably be right. But he kept going. He had to complete the pattern. By the time he’s got to the Ben Shahn drawings, it’s just getting fanciful. If you build up too detailed a story, you’ll find it irresistible to believe, but it’s getting less and less likely all the time.

Stereotypes can be irrational. Not every inference or assumption about people is irrational, of course, but our tendency to find specific stories more believable than broader qualities is irrational. Our tendency to think that most people resemble the “most typical” members of a class is irrational. Mistaken stereotypes are what happen when people are more attracted to complete stories than to actual probability distributions.