The average rationalist IQ is about 122
In The Mystery Of Internet Survey IQs, Scott revises his estimate of the average LessWrong IQ from 138 to 128. He doesn’t explicitly explain how he arrived at this number, but it appears to be an average of the demographics norm method (123) and the SAT method (134). However, using the information in his post, the SAT method doesn’t actually yield 134 but rather 123.
Here’s the breakdown: a median SAT score of 1490 (from the LessWrong 2014 survey) corresponds to +2.42 SD, which regresses to +1.93 SD for IQ using an SAT-IQ correlation of +0.80. This equates to an IQ of 129. Subtracting 6 points (since, according to the ClearerThinking test, the IQs of people who took the SAT and remember their score is ~6 points higher than the group average) brings the adjusted IQ estimate to 123.
The ClearerThinking test also provides a way to adjust self-reported IQs. Subtracting 17 points (because people who report having taken an IQ test claim an average score of 131, but their tested average is only 114) gives an adjusted IQ of 121, based on a self-reported average of 138.
Aggregating the data across all LessWrong and SSC surveys[1] with available information, the estimates consistently cluster around 122. While some might think this is too low, it’s worth noting that an IQ of 122 is at the PhD level.
- ^
2017 SSC Survey (Link): Estimated IQ Mean = 122
From Self-Reported IQ: 122 (average reported IQ: 138.5)
From Self-Reported SAT: 122 (average SAT score: 1471.9, regressed IQ: 128 − 6 = 122)
2009 LessWrong Survey (Link): Estimated IQ Mean = 125
From Self-Reported IQ: 125 (median reported IQ: 142)
2011 LessWrong Survey (Link): Estimated IQ Mean = 123
From Self-Reported IQ: 123 (average reported IQ: 140)
2012 LessWrong Survey (Link): Estimated IQ Mean = 122.5
From Self-Reported IQ: 122 (average reported IQ: 138.7)
From Self-Reported SAT: 123 (average SAT score: 1485.8, regressed IQ: 129 − 6 = 123)
2013 LessWrong Survey (Link): Estimated IQ Mean = 121.5
From Self-Reported IQ: 121 (average reported IQ: 138.2)
From Self-Reported SAT: 122 (average SAT score: 1474, regressed IQ: 128 − 6 = 122)
2014 LessWrong Survey (Link): Estimated IQ Mean = 122
From Self-Reported IQ: 121 (average reported IQ: 138.25)
From Self-Reported SAT: 123 (median SAT score: 1490, regressed IQ: 129 − 6 = 123)
2023 LessWrong Survey (Link): Estimated IQ Mean = 121.5
From Self-Reported IQ: 118 (average reported IQ: 135.4)
From Self-Reported SAT: 125 (median SAT score: 1520, regressed IQ: 131 − 6 = 125)
I think that the way that Scott estimated IQ from SAT is flawed, in a way that underestimates IQ, for reasons given in comments like this one. This post kept that flaw.
I agree. You only multiply the SAT z-score by 0.8 if you’re selecting people on high SAT score and estimating the IQ of that subpopulation, making a correction for regressional Goodhart. Rationalists are more likely selected for high g which causes both SAT and IQ, so the z-score should be around 2.42, which means the estimate should be (100 + 2.42 * 15 − 6) = 130.3. From the link, the exact values should depend on the correlations between g, IQ, and SAT score, but it seems unlikely that the correction factor is as low as 0.8.
Your argument assumes a uniform prior, but a Gaussian prior is more realistic in this case. In practice, IQ scores are distributed normally, so it’s more likely that someone with a high SAT score comes from a more common IQ range than from a very high outlier. For example, say the median rationalist has an SAT score of +2 SD (chosen for ease of computation), and the SAT-IQ correlation is 0.80. The IQ most likely to produce an SAT of +2 SD is 137.5 (+2.5 SD). However, IQs of 137.5 are rare (99.4%-ile). While lower IQs are less likely to achieve such a high SAT score, there are more people in the lower IQ ranges, making it more probable that someone with a +2 SD SAT score falls into a lower IQ bracket.
This shift between the MLE (Maximum Likelihood Estimate) and MAP (Maximum A Posteriori) estimates is illustrated in the graph, where the MLE estimate would be +2.5 SD, but the MAP estimate, accounting for the Gaussian prior, is closer to +1.6 SD, as expected. (You may also be interested in my reply to faul_sname’s comment.)
I don’t think that works unless Less wrong specifically selects for high SAT score. If it selects for high IQ and the high SAT is as a result of the high IQ then you would have to go the other way and assume an SD of 3.03.
If, as seems more likely, Less wrong correlates with both IQ and SAT score, then the exact number is impossible to calculate, but assuming it correlates with both equally we would estimate IQ at 2.42 SD.
By this logic, if rationalists are selected based on IQ and not height, and the average rationalist height is +1.85 SD, then we’d have to assume that rationalists’ IQ is +9.25 SD (assuming an IQ-height correlation of 0.2), which is, of course, impossible.
For another example of why this logic doesn’t work, consider this: if you have a variable that is uncorrelated with IQ (r = 0), and rationalists are just slightly above average for that variable, then we’d be forced to conclude that rationalists are infinitely smart (or, if they’re below average, infinitely dumb) depending on the direction of the deviation. This is clearly nonsensical.
For an explanation of why this logic doesn’t work, see my reply to Unnamed’s comment. And for the correct calculations, see my reply to faul_sname’s comment.
Indeed if rationalists were entirely selected by IQ and nothing else, and there were no other confounders, and height was +1.85 SD, IQ would be +9.25 SD. In the real world this instead provides a Bayesian update that you were wrong in assuming rationalists were purely selected for by IQ, and not e.g. gender.
The fact that going from 2.42 SD to 3.03 SD is nonsensical does not in anyway make it more sensible to go from 2.42 to 1.93. Your response to faul_sname is completely irrelevant because it assumes rationalists are selected for on SAT, which is clearly false. The correct calculation is impossible to make accurately given we are missing key information, but we can make some estimates by assuming that rationalists are selected for something that correlates with by IQ and SATs and guessing what that correlation is.
Or to put it another way: these SAT scores are compatible with an average IQ anywhere between + 1.93 to + 3.03 SD. Insofar as your prior lies somewhere between these two numbers, and you don’t have a strong opinion on what precisely Lesswrong selects for it’s not going to update you very much in either direction.
I don’t buy the way that Spencer tried to norm the ClearerThinking test. It sounds like he just assumed that people who took their test and had a college degree as their highest level of education had the same IQ as the portion of the general population with the same educational level, and similarly for all other education levels. Then he used that to scale how scores on the ClearerThinking test correspond to IQs. That seems like a very strong and probably inaccurate assumption.
Much of what this post and Scott’s post are using the ClearerThinking IQ numbers for relies on this norming.
It occurs to me that the ClearerThinking data provides a way to check this assumption. It included data from 2 different groups, crowdworkers and people in Spencer’s social network. If college-degree-level crowdworkers did just as well on the ClearerThinking test as college-degree-level people in Spencer’s network, then it becomes more plausible that both did about as well as college-degree-level people in the general population would have. Whereas if the college-degree-level crowdworkers and Spencer’s network people scored differently, then obviously they can’t both match the college-degree-level general population, so there’d be an open question about how the groups compare and direct evidence against the accuracy of Spencer’s method of norming the test.
I like that new Scott Alexander estimate of 128, 130+ always stroke me as too high, just from knowing a bunch of people irl who range from 85 to 147, and meeting a bunch of rationalists irl. The average rationalist is definitly considerably smarter than those I know who test around 120, but not as bright as the 140+ people.
The odd thing is I have met a few people in the 130ish range who had way higher computing power than normal for their IQ, so I think there probably is something like effective IQ, which is your raw base IQ (or g for that matter), multiplied by how effective your thought doctrines are. Someone with a good grasp on Bayesianism or another very good logic framework can run circles around someone with a 5 points higher IQ and less formal training in thought.
The second paragraph puts into words something I’ve noticed but not really mentally formalized before. Some anecdotal evidence from my own life in support of the claims made in this paragraph: I’ve met individuals whose tested IQ exceeds those of other, lower but not much lower, IQ individuals I know who are more educated / trained in epistemological thinking and tangential disciplines. For none of the individual-pairs I have in mind would I declare that one person “ran circles around” the other, however, the difference (advantage going to the lower but better “trained” IQ individual) in conversational dynamics were notable enough for me to remember well. The catch here is the accuracy of the IQ claims made by some of these individuals, as some did not personally reveal their scores to me.
Honestly, this fits my intuition. If I think of all the rationalists I know, they feel like they are on average near 120 IQ, with what feels like a standard distribution around it, though in reality it’s probably not quite normal with a longer upper tail than lower tail, i.e. fewer 90s than 150s, etc. Claims that the average is much higher than 120 feel off to me, relative to folks I know and have interacted with in the community (insert joke about how I have “dumb” friends maybe).
are you correcting for the year the test was taken? The SAT grading has shifted dramatically over time.
This is a good point. I don’t think it should make that much of a difference given how young LessWrong is on average, but it can’t hurt to try.
My two problem are 1) finding SAT statistics for nationally representative samples, and not just seniors that take the SAT (the latter are obviously selected) is difficult, and 2) I’d need more detailed data than just the SAT averages—I’d have to adjust each person’s SAT z-score based on the year they took the test.
I don’t think this is a valid way of doing this, for the same reason it wouldn’t be valid to say
Those are the real numbers with regards to height BTW.
These both seem valid to me! Now, if you have multiple predictors (like SAT and height), then things get messy because you have to consider their covariance and stuff.
That reasoning as applied to SAT score would only be valid if LW selected its members based on their SAT score, and that reasoning as applied to height would only be valid if LW selected its members based on height (though it looks like both Thomas Kwa and Yair Halberstadt have already beaten me to it).
Cool, you’ve convinced me, thanks.
Edit: well, sort of. I think it depends on what information you’re allowing yourself to know when building your statistical model. If you’re not letting yourself make guesses about how the LW population was selected, then I still think the SAT thing and the height thing are reasonable. However, if you’re actually trying to figure out an estimate of the right answer, you probably shouldn’t blind yourself quite that much.
Eric Neyman is right. They are both valid!
In general, if we have two vectors X and Y which are jointly normally distributed, we can write the joint mean μ and the joint covariance matrix Σ as
μ=[μXμY],Σ=[KXXKXYKYXKYY]The conditional distribution for Y given X is given by Y|X∼N(μY|X,KY|X),
defined by conditional mean
μY|X=μY+KYXKXX−1(X−μX)
and conditional variance
KY|X=KYYKXX−1KXY
Our conditional distribution for the IQ of the median rationalist, given their SAT score is N(0+(0.8⋅1⋅(2.42−0)),1−(0.8∗1∗0.8))=N(1.94,0.36)
(That’s a mean of 129 and a standard deviation of 9 IQ points.)
Our conditional distribution for the IQ of the median rationalist, given their height is N(0+(0.2∗1∗(1.85−0)),1−(0.2∗1∗0.2))=N(0.37,0.96)
(That’s a mean of 106 and a standard deviation of 14.7 IQ points.)
Our conditional distribution for the IQ of the median rationalist, given their SAT score and height is N(0+([0.80.2][10.160.161]−1[2.421.85]),1−([0.80.2][10.160.161]−1[0.80.2]))=N(2.04,0.35)(That’s a mean of 131 and a standard deviation of 8.9 IQ points)
Unfortunately, since men are taller than women, and rationalists are mostly male, we can’t use the height as-is when estimating the IQ of the median rationalist (maybe normalizing height within each sex would work?).
Interesting how consistent the estimated mean has stayed over time.
People tend to get suspicious if you claim IQs above 125, and start analyzing data and looking for reasons to believe that the actual numbers are less. But I feel like such people really overestimate what an IQ in the 120s or 130s look like. If you go on the Mensa Forums, you will likely find that most of the comments seem rather dumb, and that the community generally appears dumber than LW.
A large number of people who report scoring in the 130s on IQ tests are not lying. If the number seems off but isn’t, then what needs updating is the impression of what an IQ in the 130s look like.
I suppose that people dislike that some high IQ people just aren’t doing very well in life, and prefer to think that they’re lying about their scores