IQ Scores: What are they good for?

Response to http://slatestarcodex.com/2017/09/27/against-individual-iq-worries/ and https://www.scottaaronson.com/blog/. This post can be read standalone.

I recently encountered two articles arguing against making too much of one’s own IQ score. Both of them mostly boil down to “IQ tests are a REALLY noisy measure of g, and on an individual level the noise is going to mask a lot of the signal”. This is totally 100% correct, and is probably responsible for most of the hand-wringing those two authors encounter.

But let’s cut past the noise: suppose you’ve taken an IQ test, and the SATs, and maybe throw in some other measures too. That’s all Bayesian evidence for your underlying g, so you can put them all together to get a hopefully-less-noisy estimate. The result tells you something about your intelligence relative to the rest of the population. What should you do with this information? In particular, if the number is lower than you’d like, what’s the right response?

There are multiple good answers to that question, most notably relative advantage - pick up an intro microeconomics text if you want to know more about that one. But in keeping with my usual policy of “don’t write things that somebody else already wrote”, I’ll focus on an answer which I haven’t seen used in this context before: strategic variance.

The Underdog Strategy

Suppose you’re in an oversimplified one-on-one basketball game with three rounds. Strictly speaking, your opponent is a better player than you: they average 24 points per round, while you average 22. But you have a trick up your sleeve: your opponent is a one-trick pony, while you have multiple play styles. One play style is conservative and consistent: in one round, you’ll score 22 points and your opponent will score 24, consistently. Your other play style is more aggressive, with more variance: in one round, your opponent will score 24, and you’ll score either 14 or 30, with a 50% chance for each.

For both play styles, your opponent averages 2 more points per round than you do. But you can still win more often than not. Here’s the strategy:

• Round 1: play aggressive. You end up ahead by 6 points (50% chance) or behind by 10 (50%).
• Round 2 & 3: If you’re ahead, play conservative; if you’re behind, play aggressive. If you wound up ahead in round 1, then you’ll play conservative for the next two rounds and win by 2. If you wound up behind in round 1, then you’ll play aggressive for 2 rounds and have a 25% chance of a comeback.
• Put that all together, and your chance of winning is 62.5%.

Despite your opponent scoring more points on average regardless of strategy, you can still win more often than not!

The example is somewhat artificial, but the idea generalizes:

• When you’re “ahead”, play conservative - avoid risk, minimize variance.
• When you’re “behind”, play aggressive - take risk, maximize variance.

The principle generalizes easily to practically any game with some way of keeping score - virtually all sports, board games, card games, and so forth. (On a side note, it also applies to bacterial chemotaxis.) Let’s apply it to real life.

The Underdog Strategy in Real Life

Suppose my goal in life is to solve some major open problem in math/science - we’ll use the P-NP problem as an example. Then my own intelligence - g, IQ, whatever measure we’re using - is a very useful indicator of how far “ahead” or “behind” I’m starting.

Consider Terence Tao - presumably he’d be starting way “ahead” by this criteria. If he spent a year or two focussed entirely on P-NP, he’d probably be one of the top 5 smartest people ever to invest that much effort in the problem. There’s a reasonable chance that he could solve it by brute force of intellect - by being smarter than anyone else who’d tried. Maybe P-NP is straightforward for anyone who’s up-to-date with known circuit complexity lower bounds and has sufficiently high g, and the problem is just waiting for someone smart enough to come along and put the pieces together. There’s a realistic chance that Terence Tao could be the first person to come along who’s smart enough.

When you look at it like that, if Terence Tao decides to seriously tackle P-NP, then just spending a year pushing current approaches would be a very reasonable starting point for him. He’s starting out “ahead”, so a conservative low-risk strategy makes sense as a first thing to try.

But what if I want to solve P-NP?

I’m smart, but I wouldn’t be in the top 100 or probably even the top 1000 smartest people who’ve tackled P-NP. I will never be able to solve P-NP by brute force of intellect, by taking the standard approaches and throwing my own intelligence at them. I am not that smart.

I’d be starting “behind” in this game, my chance of winning is low a priori, so to maximize my chances I need to add variance. In this context, that means trying weird approaches. Investing effort in tools which may or may not be useful but are definitely different from what everyone else is doing, and applying those tools to the problem. On average, any particular random thing is less likely to be the key to P-NP than lower-bounding circuit complexity. But I, personally, am more likely to solve P-NP by applying some weird technique from probability or physics or economics or even biology, than by pushing already-popular strategies. (That doesn’t mean I shouldn’t get up to date with current research, just that I shouldn’t invest much effort pushing past the cutting edge in that particular direction.)

Conclusion

One last comment to wrap it up: strategic variance only applies to binary problems, where you either clear the bar or you don’t. If your goal in the oversimplified one-on-one basketball game is to improve your average score, then variance won’t help. If your goal in life is to maximize your expected earnings, then again, variance in and of itself will not help. On the other hand, if your goal in life is to become a billionaire, then strategic variance - i.e. risk taking - will help.

Generalizing further: as humans, we tend to invest less effort than we should in high-level life strategy. Things like estimating your own g/IQ are useful mainly to inform that strategy. The more strategic you are, the more value you can extract from that information. Strategic variance is just one class of strategies. Relative advantage is the main underlying strategy - e.g. in the oversimplified basketball game, you win by exploiting your relative advantage of being able to adjust your own variance. Study relative advantage, and pay attention to which tradeoffs are cheaper for you than for others.