INTRODUCTION

The crux with IQ – so far as I understand it – is that performance across abstract reasoning tasks is correlated no matter what the tasks are. That is, being good at one type of abstract puzzle implies that you’re more likely to be good at any other such puzzle. If you got $$M$$ people to do $$N$$ puzzles and made an $$M\times N$$ matrix of their scores, and then did some SVD on it, the first singular value would account for much of the weight, and if you were to rank the rows (participants) by their weight in the first left singular vector, you’d have created something akin to an IQ score.1

The claim is then that life outcomes and being good at abstract puzzles are well correlated, even when all the obvious socio-economic factors are controlled for, and that abstract puzzle solving has considerable leverage in real life too; in fact so much leverage that we should probably go ahead and call IQ a measure of general intelligence. Put another way, accounting for life problems, is just adding more columns to the matrix above, but the results are so correlated that it wouldn’t much change the significance of the first left singular vector.

I think that the inane part of the claim is that a generally transferable aptitude can be a life advantage. It is hardly surprising, and likely true for other qualities too: grit, patience, introspection, temperance and so on. The controversial part is that IQ is supposed to be (positively) immutable, largely hereditary and ultimately representative of general intelligence: lots about that bothers me, and what follows are just a couple rebuttals which I find interesting.

REBUTTALS

Conditional IQ

Can the scores between IQ test takers be matched by unequal time advantage? Say $$A, B, C$$ have IQs, $$q_a = q_b < q_c$$ respectively. If $$A,B$$ were given a time advantage and it turned out that $$q_a \approx q_c$$, but $$q_b < q_c$$, should we still say that $$A$$ and $$B$$ have an equal IQ, or that $$C$$ has a higher IQ than both of them? I feel there is a separate question regarding whether a person is able to think in a “Turing complete” way. That is, given enough time, they will figure it out. Yet at a lower time allowance, they may fail to figure it out and may be confounded with people who would never figure it out.

This same line of argument can be applied to a whole host of advantages and/or tool use scenarios. Thinker + computer, thinker + pen and paper, thinker + Mathematica, thinker + other people, and so on. The point is that IQ ranking is probably not independent of the space of possible tool use and/or advantage scenarios, so it seems a bit arbitrary to compare scores in a specific scenario.

(Lack of) correlation with rationality

Keith Stanovich et al came up with this idea called the Rationality Quotient (RQ) 2. The crux is that the more rational person has fewer cognitive biases and therefore ceteris paribus makes better decisions. Stanovich made a test derived from a big list of cognitive biases in the style of an IQ test, and administered it to lots of people (along with an IQ test) and found – amongst other things – that rationality ala cognitive biases – poorly correlates with IQ. That is, you can have a high IQ yet be a hapless decision maker, or have exceptional judgement but merely normal IQ. Intuitively, rationality is an important part of general intelligence yet largely uncorrelated with IQ.

CONCLUSIONS

IQ is supposed to be a measure of general intelligence derived from abstract puzzles which readily transfers to problem solving more generally. I find IQ suspicious for many reasons but two practical rebuttals were given: (1) an IQ ranking may change given different test taking scenario (e.g. time and other advantages, tool use, etc), and (2) it doesn’t correlate well with rationality.

1. The method generalises to $$k$$ singular values/vectors. See here for leverage scores more generally.↩︎

2. See book The rationality quotient: Toward a test of rational thinking↩︎