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Are stereotypes statistically accurate?

Apparently there’s a debate in psychology about the accuracy of stereotypes.

Lin Bian and Andrei Cimpian write:

In his book Social Perception and Social Reality, Lee Jussim suggests that people’s beliefs about various groups (i.e., their stereotypes) are largely accurate. We unpack this claim using the distinction between generic and statistical beliefs—a distinction supported by extensive evidence in cognitive psychology, linguistics, and philosophy. Regardless of whether one understands stereotypes as generic or statistical beliefs about groups, skepticism remains about the rationality of social judgments.

Bian and Cimpian start by distinguishing what cognitive psychologists call “statistical” and “generic” beliefs about categories. This is pretty cool. Here they go:

Consider the statements below:

(1a) Fewer than 1% of mosquitoes carry the West Nile virus.
(1b) Mosquitoes carry the West Nile virus.
(2a) The majority of books are paperbacks.
(2b) Books are paperbacks.

Statements (1a) and (2a) are statistical: They express a belief about a certain number or proportion of the members of a category. Statements (1b) and (2b) are generic: They express a belief about the category as a whole rather than a specific number, quantity, or proportion. . . .

The fact that generic claims – and the beliefs they express – are not about numbers or quantities has a crucial consequence: It severs their truth conditions from the sort of statistical data that one could objectively measure in the world. . . .

This point is illustrated by the examples above. Both (1a) and (1b) are considered true: Although very few mosquitoes actually carry the West Nile virus, participants judge the generic claim (that mosquitoes, as a category, carry the West Nile virus) to be true as well. . . .

In contrast, even though (2a) is true – paperbacks are indeed very common – few believe that books, as a category, are paperbacks (i.e., [2b] is false). . . .

Bian and Cimpian continue:

These are not isolated examples. The literature is replete with instances of generic claims that either are judged true despite unimpressive statistical evidence or judged false despite overwhelming numbers . . . the rules that govern which generic beliefs are deemed true and which are deemed false are so baroque and so divorced from the statistical facts that many linguists and philosophers have spent the better part of 40 years debating them. . . .

And to return to stereotyping:

All of the foregoing applies to beliefs about social groups as well. . . . The distinction between statistical and generic beliefs is operative regardless whether these beliefs concern mosquitoes, books, and other categories of non-human entities, or women, African Americans, Muslims, and other categories of humans.

And, the punch line:

Generic beliefs about social groups, just like other generic beliefs, are typically removed from the underlying statistics.

Statistics vs. stereotypes

Bian and Cimpian follow up with two examples:

More people hold the generic belief that Muslims are terrorists than hold the generic belief that Muslims are female. However, there are vastly more Muslims who are female than there are Muslims who are terrorists. . . .

Compare, for instance, “Asians are really good at math” and “Asians are right-handed.” Many more people would agree with the former generic claim than with the latter, while simultaneously being aware that the statistics go the opposite way.

OK, let’s unpack these. Here the statistics are so obviously counter to the stereotype that there has to be something else going on. In this case, I’d say the relevant statistical probabilities are not that Muslims are likely to be terrorists, or that Asians are more likely to be math whizzes, but that Muslims are more likely than other groups to be terrorists, or that Asians are more likely than other groups to be math whizzes. Maybe these statements aren’t correct either (I guess it would all depend on how all these things are defined), but that would seem to be the statistics to look at.

The stereotypes of a group, that is, would seem to be defined relative to other groups.

This does not tell the whole story either, though, as I’m sure that lots of stereotyping is muddled by what Kahneman and Tversky called availability bias.

Bian and Cimpian continue—you can read the whole thing—by discussing whether stereotypes should be considered as “generic beliefs” or “statistical beliefs.” As a statistician I’m not so comfortable with this distinction—I’m inclined to feel that generic beliefs are also a form of statistical belief, if the statistical question is framed the right way—but I do think they’re on to something in trying to pin down what people are thinking when they use stereotypes in their reasoning.

P.S. I sent the above to Susan, who added:

The issues you’re raising are ones that have been discussed a fair amount in the literature. Some of these ideas have been studied with experiments, but others have not (i.e., they’ve been discussed but not formally tested).

I agree that statistical info goes beyond just P(feature|category) (e.g., P(West Nile Virus|mosquito). As I think you’re saying, one could also ask: what about distinctiveness, which is the opposite — P(category|feature) (e.g., P(Mosquite|WNV)? Although distinctiveness can make a generic more acceptable, generics need not be distinctive (e.g., “Lions eat meat”; “Dogs are 4-legged”; “Cats have good hearing” are all non-distinctive but good generics). There are even properties that are relatively infrequent (i.e., true of less than half the category) and are non-distinctive, but make good generics (e.g., “Ducks lay eggs”; “Goats produce milk”; “Peacocks are colorful”). Finally, there are features that are frequent and distinctive but don’t (ordinarily) make good generics (e.g., “People are right-handed”; “Bees are sterile”; “Turtles die in infancy”).

I think that people are doing some assessment of how conceptually central a feature is, where centrality could be cued by any of a number of factors, including: prevalence, distinctiveness, danger/harm/threat (we have data on this as well — dangerous features make for better generics than benign features), and biological folk theories (e.g., features that only adults have are more likely to be in generics than features that only babies have — e.g., we say “Swans are beautiful”, not “Swans are ugly”).

This in turn gives me two thoughts:

1. Why we think swans are beautiful . . . that’s an interesting one, I’m sure there’s been lots written about that!

2. “People are right-handed” . . . that’s a great example. We are much more likely to be right-handed, compared to other animals (which generally have weak or no hand preference). And the vast majority of people are righties. Yet, saying “people are right-handed” odes seem wrong. On the other hand, if 80% of cats, say, were right handed, maybe we’d be ok saying “cats are right handed.” I guess there must be some kind of Grice going on here too.

P.P.S. In comments, Chris Martin points to further responses by Jussim and others.

52 Comments

  1. Jonathan Harris says:

    When I was in academics an Indian colleague would observe that a lot of Americans thought Indians are smart. He said that if they went to India they would see that there are plenty of dumb Indians.

  2. leoboiko says:

    The Pirahã language and culture seem to lack not only the words but also the concepts for numbers, using instead less precise terms like “small size”, “large size” and “collection”. And the Pirahã people themselves seem to be suprisingly uninterested in learning about numbers, and even actively resistant to doing so, despite the fact that in their frequent dealings with traders they have a practical need to evaluate and compare numerical expressions. A similar situation seems to obtain among some other groups in Amazonia, and a lack of indigenous words for numbers has been reported elsewhere in the world.

    […]

    Sometimes, people are just avoiding more cumbersome modes of expression — “Xs are P-er than Ys” instead of (say) “The mean P measurement in a sample of Xs was greater than the mean P measurement in a sample of Ys, by an amount that would arise by chance fewer than once in 20 trials, assuming that the two samples were drawn from a single population in which P is normally distributed”. But I submit that even most intellectuals don’t really know how to think about the evaluation and comparison of distributions — not even simple univariate gaussian distributions, much less more complex situations. And many people who do sort of understand this, at some level, generally fall back on thinking (as well as talking) about properties of group prototypes rather than properties of distributions of individual characteristics.

    If you’re one of the people who find distribution-talk mystifying, and don’t really see why you should have to learn it, or perhaps think that you’re just not the kind of person who learns things like this — congratulations, you now know exactly how (I imagine) the Pirahã feel about number-talk.

    (Mark Liberman, The Pirahã and us)

    • Keith O'Rourke says:

      Thanks for this.

      I think many of us could benefit from this-
      “If you’re one of the people who find XXXX-talk mystifying, and don’t really see why you should have to learn it, or perhaps think that you’re just not the kind of person who learns things like this — congratulations, you now know exactly how (I imagine) the Pirahã feel about YYYY-talk.”

      For me one XXXX would be likelihood – as functions of parameters and given observations that (along with the prior if given) sets out statistical science mathematically) with YYYY being (sufficient) estimates and their inverse variance weighted combinations (e.g. linear regression) – some details here https://errorstatistics.com/2016/08/02/s-senn-painful-dichotomies-guest-post/#comment-141927

    • Martha Smith says:

      Thanks, Leo. I often wonder how much such things are cultural and how much individual — that is, how much something like finding distribution-talk mystifying is truly individual and how much is background. I have wondered about this since I was a small child. One incident in particular sticks with me: When I was about seven years old (and for many years afterwards), I bit my fingernails. My mother often tried to get me to stop, but I had no interest in doing so. Once she said (presumably in an effort to “motivate” me), “If you stop biting your fingernails, I’ll buy you a manicure set.” I said, “OK” — reasoning that if by some quirk of nature (since I had no intention of deliberately trying) I did stop biting my nails, I would have a new toy to play with, and if I didn’t stop (which seemed most likely), there was nothing lost. The next day she came home from shopping and said, “Here’s your manicure set.” I thought she was so dumb — she hadn’t said, “If I buy you a manicure set, will you stop biting your nails?” In other words, at age 7, I understood the difference between a statement and its converse. But even though she was more than thirty years older than me, she didn’t.

      • Alex Gamma says:

        I’m not convinced. It seems that it was you who didn’t understand something: how sentences like “If you stop biting your fingernails, I’ll buy you a manicure set” are understood in conversational logic.

        • Martha (Smith) says:

          I suspect that “understood in conversational logic” may be relative to the sociological or cultural context. In this case (a seven-year-old and a parent), I would argue that the relevant cultural context would be the family. And when my father said, “If you don’t get up those stairs right now, you’re going to get a spanking,” I got up the stairs pronto — and did not get a spanking.

  3. Dale Lehman says:

    I think there is a related issue that may be more important. Generics and stereotypes typically (another stereotype?) reduce a multidimensional description to a unidimensional one. Even if Asians are good at math (whether that is true in some absolute sense or relative to other groups), Asians vary in many dimensions from each other. The recent book The End of Average by Todd Rose makes a good case for there not being such a thing as the “average” student or “average” air force pilot, etc. Once a multidimensional view is taken of the individual, there may be nobody that is average. I think stereotypes are a form of thinking of the “average.” So, if someone says “Asians are good at math” they may be thinking that “on average, Asians are good at math.” While this may lead to a statistically verifiable hypothesis, I think the more important point is that it reduces Asians to a single dimension – math ability. For me, the more important phenomenon is the need/desire/propensity of people to take one dimensional views of other people. That is the essence of stereotyping.

  4. Jon says:

    An ethical question: Suppose it were the case that it were economically efficient to use ethnic stereotypes in making a hiring decision, should it be permissible? My belief is in a reasonably prosperous society, the answer is no.

    Such a consideration could occur if different groups produce different fractions of top and bottom performers and an employer has considerable uncertainty in distinguishing between the two without considerable costs, i.e. hiring someone and risk having them fail.

    This of course leads to more “gray line” questions as to what personal characteristics are fair to be permitted to use. If a person of low intelligence can do the job, but someone with high intelligence is more likely to succeed, we probably would accept using the intelligence as a criterion.

    • Bill Harris says:

      @Jon: I’ve wondered about that myself. In Bayesian terms, the stereotypes might be seen as a (often pretty bad) prior: “You look / think / believe differently than I do => you must be lazier / dumber / less productive than I am.”

      Perhaps the ethical prior in this case is values based: “Our society believes in diversity and in giving everyone a fair opportunity,” which is roughly equivalent to “innocent (until proven guilty)” or “competent (unless data about you shows otherwise [through the likelihood]).”

      We (or some of us) sometimes speak of priors as “prior beliefs,” right? There’s nothing really new in this comment, except that it might help some who think it’s simply common sense to incorporate their stereotypes into decision making to consider reformulating their common sense (their priors) on the basis of ethical values.

    • Harald K says:

      It isn’t only stereotypes that may be statistically justified that cause ethical dilemmas.

      Say you have ten male candidates and ten female candidates, and from public data you are confident that men and women are equally likely to do well at this job. However, when judging the people in front of you, you are better at telling a competent man from an incompetent man. What do you do?

      It’s one of the many situations where you face pressure to use the best information you have, even though on a meta level you know that the information you have is biased.

      • Martha (Smith) says:

        This seems like an artificial scenario — how would you know that “you are better at telling a competent man from an incompetent man”?

        • Harald K says:

          If you have trouble imagining that, try culture instead of sex. People from your own culture express confidence one way, people from that other culture don’t seem to express it at all. You are good at communicating your way, they’re good at communicating their way – maybe. It’s hard for you to tell.

          Even simpler, make it about trust instead of competence. Say it’s a job that’s not demanding, except that you really need to be able to trust the one doing it. Isn’t it easier to be confident of your trustworthiness appraisal of someone from your own culture?

          I don’t think it’s artificial at all, I think it’s more like the default scenario.

          • Martha (Smith) says:

            @Harald:
            “Isn’t it easier to be confident of your trustworthiness appraisal of someone from your own culture? “

            It may be — but confidence is not the same a competence. That is, just because you are confident of your appraisal does not mean your appraisal is accurate. Your confidence is subjective; accurate is objective.

  5. There seems to be some linguistic confusion here as well. For example “Mosquitos Carry the West Nile Virus” is a 100% true statement when taken to be the answer to the question “What kind of insects are responsible for transmitting West Nile Virus?” similarly “Books are Paperbacks” is a 100% true statement when taken to be the answer to “I keep hearing someone say that they are going to go buy some paperbacks, what the heck kind of thing is a paperback?” (though normally you’d say “Paperbacks are books” it does work the other way as well)

    • gdanning says:

      Exactly. Moreover, the statement, “mosquitos carry the West Nile Virus” is also likely to be read as, “The West Nile Virus is carried by mosquitos,” which is of course also 100% true.

      • This raises the question of what we do with the stereotype (or whatever you want to call it). We do not behave towards all books as though they might be paperbacks. But we have behaved towards all mosquitoes as though they might be carrying the West Nile virus. The difference probably has something to do with salience, as Susan suggests.

        • I think it has more to do with bayesian decision theory: what is the “Cost” associated with incorrectly classifying a mosquito as dangerous? (hint: very small) what is the cost of incorrectly classifying a mosquito as NOT dangerous? (hint: very large) What does this imply about the decision you should make classifying mosquitos?

          how does this compare to books?

  6. The phrasing of all this, except for Susan’s comment, seems very vague. If I were stopped on the street and asked, I would state that (1b) is true, not because I’m unaware that the vast majority of mosquitos don’t carry West Nile virus, but because it allows a distinction with animals that can’t carry it. Similarly, I would say that the statement “humans give birth to live young” is true, even though it actually applies to a minority of the population (namely, the subset of women who have children). Perhaps the authors are really claiming that people who say yes to “Mosquitoes carry the West Nile virus” and “Asians are really good at math” actually think that *every* mosquito carries the virus and every Asian (or even the majority) is good at math. I’m skeptical. I suspect that there is data out there on this claim.

  7. Anoneuoid says:

    I’ve always been partial to the idea that there is a limit to the number of representations that a human can store/access (eg, Dunbar’s number*, but I am not tied to that specific number or evidence), and stereotypes are just the name for the heuristics most commonly used in the face of that obstacle.

    *https://en.wikipedia.org/wiki/Dunbar%27s_number

  8. Chris M says:

    Lee Jussim responded to the Bian and Cimpian article here:
    http://www.spsp.org/blog/stereotype-accuracy-response

    It’s long but worth reading in full.

    One problem with stereotypes arises in part due to the English language. Both of these statements are true:
    Giraffes are taller than ants
    Men are taller than women

    This is because “taller” is vague and can refer to averages or complete sets. Someone who knew nothing about humans–an English-speaking alien perhaps–could misinterpret the second statement. However, I believe most people comprehend it in the way the speaker intended.

  9. Rahul says:

    The example seems odd. Rather than a generic-claim issue isn’t this mostly about the semantics of “carry” vs. “are”?

    Sure, people judge (1b) is true but not (2b) but that’s because it makes sense: the operative word in (1b) was “carry” vs in (2b) it was “are”.

    Mosquitoes carry the West Nile virus. Just like Trains carry people. (But *not* all trains carry people)

    OTOH, “are” is interpreted more in the sense of a sub-set. Paperbacks are books. But *not* “books are paperbacks”. That’s like “Dogs are animals” but not “Animals are dogs”.

    In other words, isn’t this more about semantics than stereotypes?

  10. Paul Alper says:

    Is the problem confined to the English language? Recall the admonition: If you want to make love, speak French. If you want to interrogate a prisoner, speak German and if you want to confuse, speak English.
    Gerd Gigerenzer has pointed out that the English “and” is not the necessarily the same as the logical AND: “I invited friends and colleagues to the party” is interpreted as “I invited friends or colleagues to the party.” Likewise, the answer to the waiter’s question, “Do you want cereal or eggs for breakfast?” is not “Yes.”

    • leoboiko says:

      Speaking as a linguist, trust me that I could write a ten thousand rant about how completely and utterly wrong that admonition is. I’ll spare everyone the trouble, and give the short answer: no, this kind of thing isn’t confined to the English language, but happens with literally every single human language on Earth.

      And human words like “and”, “if”, “not” are definitely not the same things as the technical operators of formal logic, anymore than “for” and “while” are the same as the C++ operators; and why should they be? That’s not even a “problem”. Human languages are different kinds of things than mathematical formalisms.

      • Corey says:

        A mathematical urban legend: when the logician Carnap was immigrating to the US he was asked during the usual consular interview, “Would you favor the overthrow of the US government by violence or force of arms?”. He thought for a while, and responded, “I would have to say force of arms…”

        (source)

      • Paul Alper says:

        But English has its own intrinsic type of problems. Consider the elementary riddle of my youth:

        “The beggar has a brother but the beggar’s brother has no brother.”

        Said riddle does not exist in French, German, Spanish or Norwegian (and I assume not in Portuguese either), because “begger” carries extra information when dealing with a female. Also, there is no such thing as a French, German, Spanish or Norwegian National Spelling Bee because these languages are (mostly, more or less) phonetic. And perhaps only in English would the sentence “Human languages are different kinds of things than mathematical formalisms” be criticized on the grounds that “different …from” is preferred to “different …than.”

        • leoboiko says:

          I don’t really get what it is that you’re hinting at. Do you think English is a special kind of language because the word “beggar” has no intrinsic gender? If anything, it’s the other languages you listed which are weird, by forcing their equivalent of “beggar” to encode a gender; the majority of languages in the world are like English in that they have no grammatical gender In any of those majority of languages, you could make an equivalent of the beggar riddle.

          And then you said that German and Spanish are “mostly” phonetic, while seemingly implying that English is not phonetic, or perhaps less phonetic. That doesn’t make any sense. All of the languages you’ve cited are 100% phonetic. All you have to do is to produce the sounds of English around a toddler for three or four years, and they’ll become a native English speaker, just like they’d become of German or French. Every human language is either phonetic, like English, or signed, like American Sign Language. I think you’re confusing natural languages with writing systems. A writing system is not a language; it’s merely a kind of technology that serves for recording the language in a visual medium, like a vinyl disc or a spectrogram can represent sound spatially. Now, it’s true that the English writing system is particularly complex, because it’s especially outdated, being based on the sounds the language had centuries ago (though French rivals English in its outdateness ; consider that it still writes long-silenced plurals, or that it records ancient long vowels as circumflexes which are now meaningless, or that ‹e› can be pronounced all of /e/ /ɛ/ /ə/ or nothing, or that the word ‹oie› is now pronounced /wa/—not a single sound of the original spelling is left in the current pronunciation!) Be that as it may, the complexity of a writing system is entirely unrelated to the features of the language. You could write English in the phonetic alphabet, or in a new phonetic spelling, or in Arabic letters or Tengwar or anything else, and it’d be as regular as you wanted; and a spelling reform would have the obvious impacts in spelling bees, school education and other social institutions. Japanese writing is orders of magnitudes more complex than English; the Japanese character test, Kanken, is a lot more basic than a spelling bee, merely testing one’s ability to recall the character themselves – more than 6000 of them – and getting a passing grade is considered to be an impressive feat for literate adult. If the Japanese decide to simplify their writing (like the Koreans or the Vietnamese did), these tests, and the entire publishing segment of “how to memorize characters”, would disappear, just like English spelling bees would if they used a simpler notation for their language. None of this has any bearing on the language itself, or in their relationship to mathematical ideas. A language is a set of words and a grammar (a set of rules about how to combine these words); a writing system is a notation system, no more than a way of setting language down.

          As for the from/than distinction, well, of course this particular distinction is specific to English. My error is a direct consequence of me not being a native speaker, and not having this distinction in my language. But all languages have their own similar distinctions and preferred co-occurrences (“collocations”). If you’re not a native Portuguese speaker, and you try to learn it right now, you’ll have some trouble keeping up with the ser/estar distinction (both “to be” in English), just like I had difficulty with “from/than”. If you tried Japanese, you’d have trouble with wa/ga, both of which correspond to the subject position in English. In Tupi, you’d have to take care to distinguish exclusive, inclusive, and all-inclusive first-person plural, etc.

          To go back to the topic of this post: a) No, the kind of ambiguity under discussion here (1a/1b and 2a/2b in the original post) is not at all a special feature or weakness of English, but something common to human cognition and present in all languages; and, b) No, English isn’t particularly “more confusing” than any other human language, nor is German more aggressive or French sexier, or any other sort of projected national stereotype. German Romantics writing love poetry sound perfectly romantic to German ears, French logicians writing treatises sound dry and dull to French ears, and I’m confused by a bad writer in my native language (or any other), not by the English of a good writer.

          • Ben says:

            Also +1. and thanks for saying it so well.

          • Paul Alper says:

            The word “phonetic” seems to have two meanings, thus another instance of ambiguity to add to the above statements, (1a), (1b), (2a) and (2b). Perhaps to a linguist,

            “Every human language is either phonetic, like English, or signed, like American Sign Language.”

            To most of us, however, phonetic is defined this way: https://www.englishclub.com/esl-articles/200104.htm

            “That means you can look at a written word and know how to pronounce it. Or you can hear a word and know how to spell it. With phonetic languages, there is a direct relationship between the spelling and the sound. It is important to understand that English is not a phonetic language. So we often do not say a word the same way it is spelled. Some words can have the same spelling but different pronunciation.”

            • The thing you are talking about is a feature of the spelling system, which is a kind of attachment to languages. Most languages do not even have spelling systems. Would you say these are phonetic or not? It makes little sense. Then of course many languages have multiple spelling systems. English has a number of commonly used ones including American and British spellings (and Canadian and Australian and New Zealandian and so on), but also various reform proposals, which tend to be very phonemic. Notice the difference. Spelling systems follow the phonemes, not the phones (that would be horribly inefficient and difficult!). It’s for the same reason that the principle you are referring to is called The Phonemic Principle, not the Phonetic. There’s also IPA which is of course very phonetic and which is used for just about all spoken languages.

              So yes, the dispute is because of the multiple meanings of “phonetic”, but I think that if you take the time to read up a bit on linguistics, you will agree that it is confusing to use the word as you did, even if this usage is found among non-experts.

        • Harald K says:

          I have never heard a female form of beggar (“tigger”) in Norwegian. I have indeed heard the riddle in Norwegian, although with another word.

          Like in English, there are occupational or role descriptions that have gendered variants (e.g. host/hostess – “vert/vertinne”) but most don’t. It’s quite independent of grammatical gender.

  11. Dave says:

    I saw a talk on this in May that gave an extremely elegant theory of generics, with data to (apparently) back it up: http://arxiv.org/abs/1608.02926

  12. Jonathan says:

    I had a girlfriend who one day told me all Jews are rich. I tried to explain to her – why did I bother? – that isn’t true but I realized she was well off, went to a fancy private school and so in her world the people she identified as Jewish were pretty well off and that was her lousy statistical conclusion. I’ve since met people who don’t know any Jews at all – at least not to their knowledge – and even people who have met only relatively poor (and/or elderly) Jews in their culture but who also say all Jews are rich. The statistical connection in these cases is in one sense much more attenuated and sometimes runs counter to actual observed evidence but it is still “statistical” in the sense that everyone knows this is true so therefore it must be true.

    These are two types: an inference drawn from actual observations that is inappropriately stuck on to a larger population versus an inference drawn from shared inferences. Both are a kind of objectivity: the first is drawn from life but then fails when extended while the latter is a shared objectivity that also fails when tested against data. Both can have absurd power. As in, there are a number of cases – France, for example – where poor Jews have been kidnapped with large ransoms demanded because everyone knows Jews have money even when the guy kidnapped lives in your poor neighborhood and you know the family.

    This interests me because we share inferences all the time and construct objective beliefs and these have lasting power. The massively stupid staying power of Galen’s medicine, for example, which actually prevented – along with religion – the rise of facts outside the Galen framework. Not to be deconstructionist, but much of life is shared objectivity that isn’t true outside our shared frame.

    • David Condon says:

      Um, if taken to refer to the relative claim, then the statement “jews are rich” is true. Or if all is taken to mean the majority then that claim is also true.
      http://www.pewforum.org/religious-landscape-study/income-distribution/

      • Jonathan says:

        Well no. Per the Pew graph, Jews are relatively “richer” income-wise in the top quarter than Hindus, but Hindus do better when counting the top half and 31% of Jews are still below $50k, with half of those below $30k. I don’t see a statement that “all Jews are rich” as a relative claim on the order of “Jews do better economically than many groups”, in part because the latter has many complexities including the relative population sizes, locations (e.g., NYC incomes are higher than Utah incomes in general), etc. The statement “all Jews are rich” would make me ask why there are so many Jewish charities to help poor Jews – as in, why are they neede? – while the statement than “Jews do better …” is actually an explanation for why there are so many Jewish charities to help poor Jews.

  13. Sam Gross says:

    Small typo: “Yet, saying “people are right-handed” odes”
    odes -> does

  14. Deniz Rudin says:

    There’s some interesting work being done right now by Stanford’s CoCoLab about when (and how strongly) people will endorse generic statements. A recent paper of theirs is available here:

    http://stanford.edu/~mtessler/papers/Tessler2016-cogsci.pdf

  15. Paul Alper says:

    For those of us who have no idea what is the meaning of

    “I guess there must be some kind of Grice going on here too.”

    go to

    https://faculty.washington.edu/smcohen/453/GriceMeaningDisplay.pdf

  16. maxim says:

    Not sure if it matters, but there is a recent article in Stanford Encyclopedia of Philosophy called “Generic Generalizations”

    http://plato.stanford.edu/entries/generics/

  17. Chris J says:

    The distinction being made between statistical and generic looks like a matter of degree. Statistical seems to refer to the lower end of the spectrum, like the 1% of mosquitoes, which, in any reasonable person, begs for more information in order to make a rational decision – but how many mosquitoes are in these woods? Are there thousands? What is the likelihood of a bite? Do infected mosquitoes bite more than non-infected?
    Generic suggests the percentage is high enough to be treated as universal. Sixty percent of the deer ticks in these woods carry lime disease. OK, let’s call it 100% for decision-making purposes.
    We can end up making bad decisions based on stereotypes, both positive and negative stereotypes.
    Unfairness arises at both ends of the spectrum when we apply this to people. “Asians are good in math” may be true in group comparisons, but when would that ever be useful information to make a decision based on individual comparisons that is not superseded by other more useful data and plenty of time to react? Not in hiring. Not in college acceptances.
    A particular generic stereotype may be true 60% of the time. Some people do not care if the other 40% is unfair to an identifiable group. In extreme cases of feeling safe, they may not care about only being correct much less than 1% of the time. People have a hard time understanding really low probabilities or really low percentages in general. As a group, are Asians less fearful of terrorism? After all, they are good in math.
    Consistent with Dale Lehman’s comment, the issue is how much people feel the need to acquire and process new and useful data and the propensity to abandon that stereotype when warranted. If there is a debate in psychology now about the accuracy of stereotypes, the national political backdrop could be a factor. The distinction between generic and statistical stereotypes may be a proxy for the distinction between (a)close-mindedness and (b)open-mindedness. Both the Republican and Democratic conventions recognized the power of stereotypes and brought in non-politicians to address the gatherings. The Republicans brought in speakers who were victims of violent crimes by immigrants to reinforce a stereotype of immigrants as criminals, which to my knowledge, is not necessarily a widely held stereotype. The Democrats, as is now famous, brought in parents of a fallen soldier who are Muslims to debunk the negative stereotypes of Muslims. The Democrats have the easier logical case to make because you only need one example to show that the generalization is false. Still, there are very few war heroes, period. So the more persuasive case, statistically, would be made by a Muslim teacher, nurse, or office worker who is one of millions.

  18. MH Tessler says:

    How cool to see a discussion of generics on this blog. And how timely as well. I’ve just posted a pre-print of a contemporary, computational psycholinguistic analysis of generics that I’ve been working on for a few years with Noah Goodman at Stanford. Can be found here: http://arxiv.org/abs/1608.02926

    I’ll summarize the main points, starting with something Andrew wrote:

    “In this case, I’d say the relevant statistical probabilities are not that Muslims are likely to be terrorists, or that Asians are more likely to be math whizzes, but that Muslims are more likely than other groups to be terrorists, or that Asians are more likely than other groups to be math whizzes. Maybe these statements aren’t correct either (I guess it would all depend on how all these things are defined), but that would seem to be the statistics to look at.”

    “As a statistician I’m not so comfortable with this distinction—I’m inclined to feel that generic beliefs are also a form of statistical belief, if the statistical question is framed the right way…”

    This is precisely the intuition we aimed to formalize. We thought: the relevant distribution to consider is the distribution over P ( feature | category ), for categories both with and without the feature present. To a first approximation: this is a mixture distribution. Thus, the distributions are often bimodal (some categories have the feature, some don’t), and the properties of the upper-mode (the categories with the feature) are quite variable across different properties. (There are plenty of figures of these distributions in the paper).

    Our full theory is a Bayesian model of Gricean reasoning, and uses a very similar approach that has been used to explain the context sensitivity of gradable (vague) adjectives like “tall”. A 4 year old can be “tall” (while not being yet 5 feet), whereas no self-respecting 20 year old who is 5-foot would call themselves tall. The critical difference is that the distribution of heights for 4 year olds is really different than the distribution of heights for 20 year olds (or full grown humans. generally). In the same way, the distribution of P( feature | category ) for “carries malaria” looks a lot different than “lays eggs” which looks a lot different than “is female”. By considering these distributions (which we take to be people’s beliefs about the property), together with the actual P ( feature | category ) for the target category (e.g., the % of birds that lay eggs), and the general communicative principles of “be truthful”, “be informative”, the “statistical puzzles” of generic language disappear (malaria and so forth). We have a computational model that matches human truth judgments for a canonical set of “troublesome” generics that linguists and philosophers have talked about for the past 40 years. (Also, there are further predictions of the model that are tested and borne out in other experiments.)

    A final note, inspired by another Andrew remark:

    “This does not tell the whole story either, though, as I’m sure that lots of stereotyping is muddled by what Kahneman and Tversky called availability bias.”

    No doubt. We make a related point in the paper (providing some empirical validation for it as well). The actual P ( feature | category ) that we think is so fundamental is people’s subjective (and, predictive) probability (not the objective frequency). This thus ties the truth conditions of generics to speaker’s beliefs, influenced by their intuitive theories, biases, availability and so forth. In the end, we show that subjective probability is a valid way to understand generic language, without having to take too seriously the notion of “generic” as separate from “statistical”

  19. A lot of this is about what I’d call “focus”. See Arik Cohen’s work on generics (topic of his dissertation in the early 90s—he was my first Ph.D. student—and widely cited in all this literature).

    So when I say “Italians are good skiers”, I’m not focusing on all Italians, just the ones who ski. It’s like when I say “the president” — you can’t figure out who *the* president is without an implicit understanding of what the person is president of. The stats club? A Fortune 500 company? The United States? This goes back to Strawson’s criticisms of Russell’s theory of definite descriptions (“the” being the definite article in English, “a” being indefinite), long before Grice hit the scene. Same thing MH Tessler is getting at with gradable adjectives (a creature be a large ant without being a large animal).

    The other neat thing about stereotypes is that they can be used to communicate successfully even if they’re wrong. Searle (who I generally vehemently disagree with on the philosophy of mind) has a great paper on simile and metaphor. He has an example where you say things like “sweet as a kitten” and people know what you mean, even though kittens are cold-blooded killers.

  20. Oh, and when I retire, I’m going to get around to writing my pop philosophy/psychology book, Jumping to Conclusions, about how people reason mostly by association (i.e., stereotype), not by logic. This was the point Herb Simon used to drive home in his cognitive science lectures at Carnegie Mellon—our brains aren’t fast enough to carry out sequential logic, and we tend to get syllogism problems wrong, but we’re pretty darn good at reasoning by analogy. And it goes back to Wittgenstein’s notion of “family resemblance” (i.e., what is a chair? does that log count if I sit on it?) and even back to Aristotle’s attempt to define humans as featherless bipeds. So I wanted to work up from Aristotle to Rorty’s more nuanced notion of pragmatism, going through Wittgenstein and cognitive psych. I just don’t have the time or really the expertise to write it, despite having a Ph.D. in cognitive psych and having taught philosophy of language for years—this is really deep stuff and very very hard to write about in anything other than an offhand way, like in blog comments.

    All of linguistic semantics is based on analogy; what the field calls “formal semantics” is in fact usually just more syntax (with some nonsense semantics, like possible worlds theory tacked on that nobody believes in). The real action is in metaphor and analogy. Ludlow’s book on the dynamic lexicon is really eye opening if you’ve spent your life in American-driven (i.e., Chomskyan) linguistics: https://www.amazon.com/Living-Words-Meaning-Underdetermination-Dynamic

  21. Keith O'Rourke says:

    > The real action is in metaphor and analogy.
    Seems sensible to me!

    > work up from Aristotle to Rorty’s more nuanced notion of pragmatism, going through Wittgenstein and cognitive psych. I just don’t have the time or really the expertise to write it
    When I was a grad student, Ian Hacking tried to convince that one should not worry about that but rather do ones best to bring their perspective to it.

    Alternatively, you could just be distracted by other authors similar work

    Search for Rorty here (in particular page 251)
    https://books.google.ca/books?id=05TSDAAAQBAJ&dq=CAMBRIDGE+PRAGMATISM+From+Peirce+and+James+to+Ramsey+and+Wittgenstein+Cheryl+Misak&source=gbs_navlinks_s

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