A factor you don't mention is correlation between characteristics.
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, 0.99^n ->0 as n goes to infinity.
If those characteristics are positively correlated with each other, then the percentage doesn't drop as fast as 0.99^n; for example I'd expect "snobbish" to be correlated with "rich", and maybe "white" to be correlated with "smart" (from what I've heard of the American system (I never set foot in an American university myself), SAT requirements for minorities are lower than for whites).
Of course, this can be counterbalanced by negative correlations; still in this case, I'd expect non-smart students to be more likely to be rich, and non-rich students more likely to be smart.
I think part of what makes stereotypes is that people think about such things in sensory modes rather than verbally.
If you're visualizing a person (and possibly imagining hearing them talk), you've got a single image, not a bunch of alternatives or a probability distribution.
Damn, nice catch. I'm going to start being more mindful of what kinds of thinking I tend to use for various problems and the inherent biases thereof. (I actually don't think about stereotypes in sensory (visual) modes, but I used to, and I'd forgotten that it's probably the default way to think about stereotypes.)
In your example, the literal truth of Alvy's claim strongly depends on all the conjuncts being true, but the insightfulness or truth-like-ness etc. of the claim does not. If 90% of his guesses are right, that's still pretty good. I think this pattern is more general: unless a story falls apart when you take any of its components away (e.g. because it's a math proof), conjunction bias is mitigated by the fact that a conjunction can be what humans call "true" without being literally true.
Plus the more specific the claim, the more points he gets for insightfulness. Guessing that someone is left-wing doesn't get many points at all, but if Allison's father really does have Ben Shawn drawings then Alvy gets a lot.
Hmm. Sarah, are you quite sure you'd like to live in a world where people judged each other offhand based on accurate probability distributions - as opposed to a world where people judged each other "fairly" and kept a "blank slate"? If you'd prefer the latter world, then your post is not your true rejection of the idea of stereotypes.
A world where people judged each other accurately -- it might sometimes be unpleasant, yes, but I don't think I'd have the right to request people not to do it.
"Keep a blank slate" is a way of being charitable, and, yes, sometimes it may be good to be charitable, not just rational. But even before that I think that a sizable chunk of real-life stereotyping is not rational.
If they added appropriate error bars and willingness to update to the probability distributions, it might not be so awful.
And when I say "error bars", I don't just mean allowing for experimental error, I mean allowing for the possibility that the thinking which led to the probability distribution was motivated by the desire to maintain or expand a stereotype.
This one really is hard to kick. For a moment, I found myself objecting that it couldn't really be less likely for a Harvard student to be smart and rich than just rich (this is the Ivy league after all) before I mentally kicked myself and remembered that of course it's more likely to be just one than both regardless of the set you're dealing with.
I suspect that if someone makes a set of descriptions that are too specific though, eventually it's going to start dawning on them that they're narrowing their category and decreasing the likelihood that anyone is likely to fall into it. A smart rich white snobbish person might intuitively sound like a more likely Harvard student than just a rich person, but a smart rich white snobbish man with chestnut brown hair, brown eyes, straight nose, 5'11, pressed blue shirt with a popped collar.... eventually they'd realize they were getting ridiculous. It would be interesting to see how the likelihood people assign to propositions would graph against a set of qualifications that rises from low to arbitrarily high levels.
Some Harvard students are typical; but extremely typical Harvard students are rare.
See also this Anders Sandberg's post: Why normal is unusual
True normality is hence so rare that it makes you a member of a very small and odd minority.
I'm not sure I like the idea of coupling the adjective irrational with stereotypes. I think that we can talk about irrational belief in or acceptance of a stereotype - belief or acceptance not justified by evidence. We can talk about irrational use of a stereotype - letting a stereotype of poor performance overrule objective evidence of good performance at some task. But stereotypes themselves, considered as rough summaries of objective reality, are some degree of valid or invalid, rather than rational or irrational.
I realize that the posting was mostly quite properly discussing irrational construction of stereotypes and irrational use of (potentially valid) stereotypes. My quibble applies almost not at all to the article; almost entirely to the title.
i was tempted to make a hansonian post along the lines of 'racism is about status' but now that i think about it I think status is intra-tribal while racism has its roots in extra-tribal interactions. people that don't look like you don't share your genes and are thus scary competitors.
racism has its roots in extra-tribal interactions
It seems more historically accurate to say that racism has its roots in inter-tribal interactions: for instance the interactions in pre-modern Europe between Christians and {Jews, Gypsies, Moors}; the interactions in America between whites and {Native Americans, Blacks, newer white immigrants, nonwhite immigrants}; the interactions in Malaysia between Malays and {Chinese, Indians}; and so on. In each case, there is not merely a single "tribe" and its outsiders, but rather multiple "tribes" each with its own culture.
"Scary competitors" seems to be an unnecessary assumption, given cognitive biases. The coupling of fundamental attribution error + outgroup homogeneity bias + negativity bias + loads and loads of the availability heuristic, would lead people in groups to conclude that any negative (or merely confusing) experiences with other groups are representative of fundamental negative facts about those other groups.
I think "scary competitors" is relevant-- a few strangers are exotic and interesting. Prejudice kicks in when a substantial group shows up.
Re: this and your last discussion section post
You're leaving mega karma-bucks on the table by not posting to the main site. Great stuff.
a very typical Harvard student would be rich AND white AND smart AND snobbish
Do you really need the AND everywhere? Doesn't "rich OR white OR smart OR snobbish" make a stereotype as well? And you can see that in this form, adding more characteristics makes the stereotype more probable.
I meant it in the Boolean sense, and I meant AND, not OR. The conjunction fallacy is evidence of people really finding AND more believable.
Good point (how about "white AND snobbish AND (rich OR smart)"?)
Actually, we nerds may be making a mistake by literally interpreting a statement like "rich and white and smart and snobbish" as a formula of propositional logic with boolean operators, whereas actually it's being used as shorthand for "the typical Harvard student has most characteristics in the set [rich, white, smart, snobbish]".
Is it? Although from a logic point of view such a definition is better, it is my experience what when people say "rich and white and smart and snobbish" they actuall mean AND in the boolean sense. The key is that the definition should be what a generic person (ie not one of us [ie one of "them"]) would think, rather than what actually makes sense/works.
Stereotypes often have no basis in experimental data, or a very misguided inference. Example: every racial supremacy movement, ever.
Now that I think of it, stereotypes can arise from an "us vs them" separation (where, for example, "us" = "white or Aryan race" and "them" = "everyone else", or "us" = "men" and "them" = "women") and grow from arbitrary fluctuations, generalizing from very small groups or even one example, and motivated by politics.
If stereotypes are based on invalid inference, then yes, they are irrational. "Most Less Wrongians are male" is a rational stereotype; "women are inherently irrational by nature" is, ironically, an irrational stereotype.
"women are inherently irrational by nature" is, ironically, an irrational stereotype.
I disagree. It's a factual claim that may be true or false. I happen to believe it's mostly true, though I prefer the more general form "human are inherently irrational by nature".
Haven't thought of that generalization, but well, you know what is presumed by that phrasing by those who use it.
Yes, that "women are inherently more irrational than men by nature" - that may or may not be true, but I don't think it's an irrational belief. I prefer to keep the term "irrational" for things like "Well the evidence may say otherwise, but I still believe in my heart he's innocent" or "I plan to get rich by playing the lottery", or "that guy's black, so he's probably a criminal" or "since you can't prove I'm wrong, I can keep on believing" - i.e. failures of logical inference and rationality, not inaccurate beliefs on factual claims.
you can always water these things down until everyone agrees: "due to a confluence of cultural and biological factors of unknown relative weights women seem less able/inclined to rational behaviors."
yawn.
controversy is more fun (BEWARE!). I personally think that the whole women are irrational thing has to do with males just happening to be better suited to the vast divide between our current environment and the ancestral one*. Of course this is very seriously prone to the fundamental attribution error. So I would be interested to know if any women have ever thought the same thing about men.
*actually I think men had a relative advantage in farming civilizations but women will prove to have an advantage in information civilizations.
actually I think men had a relative advantage in farming civilizations but women will prove to have an advantage in information civilizations.
Why?
it wouldnt take much to argue me out of it. farming -> overwhelmingly patriarchal. information -> women continue to out pace men in educational attainment, power within organizations catches up with and then surpasses men as a result.
Women (and, more to the point, girls) outperform men and boys, on average, in verbal ability and grades up to and through college. This doesn't show up much at the highest levels of intelligence/educational attainment, where boys perform well, but it's significant in the midrange. Boys are also less likely to be compliant students (absenteeism, discipline problems, tardiness are more common with boys) which has long-term effects on their educational prospects.
Midrange colleges have to engage in significant affirmative action for boys to get a 50/50 gender balance. Women are also more likely than men to pursue post-college education of some kind. (Don't visualize a top-tier engineering PhD, visualize a midrange master's in social work.)
So, if current trends continue (more credentialization, more need for writing in the workplace, more of a culture of compliance) the average man will be at a disadvantage compared to women, even if the top men continue to earn the top salaries. (Note: I'm not sure how long these trends will continue. And I'm not sure they're good, either -- there might be bad effects to credential inflation and to stigmatizing rebellious/non-compliant attitudes.)
Most of my evidence comes from Richard Whitmire.
I'm skeptical that this is based on adequate information, but I'm not prepared to argue against it. It would take a serious in depth examination of the issue which I haven't done before I felt that I could draw a conclusion at all, rather than simply writing a contrary conclusion at the bottom line and working my way down to it.
I expect the number of women graduating college to continue to out pace men and for a significant gap to begin to develop.
This is a good and important article, but it would be improved by having a point. Examples of points are "Behold this compactly stated surprising truth I have now demonstrated" or "And that's why you should do X" or "Thus the common belief Y is dumber than a sack of bricks."
You, that's who.
No I don't. Your stereotype for 'you' is broken. (That claim interrupted my parsing of an otherwise excellent article.)
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.)
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.