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Vaniver comments on LW Women: LW Online - Less Wrong Discussion

29 [deleted] 15 February 2013 01:43AM

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Comment author: MugaSofer 20 February 2013 11:11:02AM -1 points [-]

If you believe that stereotypes are Bayesian evidence for the ground truth, then good science is more likely to match stereotypes,

That ... really doesn't follow.

Comment author: Vaniver 20 February 2013 05:09:07PM *  1 point [-]

That ... really doesn't follow.

Suppose G is a binary variable of the ground truth, S is a binary variable of the stereotype, and E is a binary variable of the result of an experiment.

If stereotypes are Bayesian evidence for the ground truth, that means P(S|G)>P(S|~G) and P(~S|G)<P(~S|~G). By "good" science, I mean science that is Bayesian evidence for the ground truth, so P(E|G)>P(E|~G) and P(~E|G)<P(~E|~G). Thus, for most distributions we get P(E|S)>=P(E|~S), and P(~E|S)<=P(~E|~S). (If you don't see why this is, I recommend opening up a spreadsheet, generating some binary distributions which are good evidence, and then working out the probabilities through Bayes.)

It's not guaranteed to be the case, because stereotypes and the results of experiments are probably not independent once we condition on the ground truth. The important thing about using this as a criticism is noting that stereotypes prevalent in academia and stereotypes prevalent in the general population may be rather different. Looking at the suggested results in the linked article, you'll note it's saying "hey, you should conform to my stereotypes, even when the ground truth is probably the other way" under the guise of "smash stereotypes."

Comment author: MugaSofer 21 February 2013 03:27:53PM *  -3 points [-]

Firstly, just because something is Bayesian evidence, it doesn't follow that it's strong enough to overcome the prior probability. We may have reason to believe that , say, we're all clones, and thus the stereotype that anyone from vat 4-G is an idiot are probably unfounded. Of course, there could be something wrong with vat 4-G, and we update our probability of this, but that doesn't make it more likely. (And the Robber's Cave experiment shows that even when two populations are drawn from the same random distribution, opposing stereotypes can and will form.)

Secondly, I suspect you may be using a more general definition of "stereotype", whereas I (and, I'm guessing, that article) are using a definition closer to "overgeneralization" or "simplistic profile of a large group", which naturally are contrasted to "normal distribution". Could you taboo "stereotype" for me, please?

Comment author: Vaniver 21 February 2013 11:03:05PM 2 points [-]

Firstly, just because something is Bayesian evidence, it doesn't follow that it's strong enough to overcome the prior probability.

Ah, that's the issue: I don't mean that it's more likely than not, or P(E|S)>P(~E|S), just that it's more likely than it would be otherwise, or P(E|S)>P(E)>P(E|~S).

I suspect you may be using a more general definition of "stereotype"

Quite possibly. What I mean by 'stereotype' is generally 'the general population noticing results from a distributional tendency.' Suppose the population holds an opinion of the form "men are smarter than women." As a logical statement, it is disproven by finding a single woman who is smarter than a single man (which is easy to do!). As a distributional statement, it could be interpreted as any of "the male intelligence mean is larger than the female intelligence mean" or "the male intelligence variance is larger than the female intelligence variance" or "high male intelligence is more visible than high female intelligence," because all of those are distributional tendencies that could have noticeable results along the lines of "men are smarter than women."

In particular, the ground truth of higher male variance in intelligence is interesting because it results in both "men are smarter than women" and "men are dumber than women" being valid impressions, in the sense that there are more smart men than smart women and dumb men than dumb women! This is perfectly natural if you think in distributions, and it seems to me that both of those are memes that are common in the wider culture.

Comment author: MugaSofer 25 February 2013 06:39:13PM *  -2 points [-]

Ah, that's the issue: I don't mean that it's more likely than not, or P(E|S)>P(~E|S), just that it's more likely than it would be otherwise, or P(E|S)>P(E)>P(E|~S).

Oh, right :)

As a distributional statement, it could be interpreted as any of "the male intelligence mean is larger than the female intelligence mean" or "the male intelligence variance is larger than the female intelligence variance" or "high male intelligence is more visible than high female intelligence," because all of those are distributional tendencies that could have noticeable results along the lines of "men are smarter than women."

Have you tried asking people what they mean? That might narrow it down.

In particular, the ground truth of higher male variance in intelligence is interesting because it results in both "men are smarter than women" and "men are dumber than women" being valid impressions, in the sense that there are more smart men than smart women and dumb men than dumb women! This is perfectly natural if you think in distributions, and it seems to me that both of those are memes that are common in the wider culture.

"X are dumber than Y" is a pretty universal "meme". Just like "X are worse people than Y", "X are more/less emotional than Y" and so on and so forth. Note that positive stereotypes of women usually emphasize their intuition, which is often seen as opposed to "intelligence".

IOW, interesting, but probably coincidence, since it fits better with the known tendency to develop opposing stereotypes than academics foolishly ignoring sources of evidence.