Bio: Steven Arthur Pinker is a Canadian-American experimental psychologist, cognitive scientist, linguist and popular science author. He is a Harvard College Professor and the Johnstone Family Professor in the Department of Psychology at Harvard University and is known for his advocacy of evolutionary psychology and the computational theory of mind.

http://www.investopedia.com/terms/t/tailrisk.asp#axzz1ey3VRCZG

http://www.wired.com/techbiz/it/magazine/17-03/wp_quant?currentPage=all

(a lot of taleb’s stuff seems to fall into this category, though benoit mandelbrot is the original source of the more general issue)

I don’t know enough of the theory here to know what is generally believed about the distribution of such heavily selected traits.

I wouldn’t call the appeal to genetic additivity as grounding an assumption of a normal curve for IQ (or g) as as being an abstract one based on purely mathematical theorem (the central limit theorem). The normality of the curve depends on certain assumptions made in the well established Mendelian model, along with assumptions as to the approximate number and size of effects of individual genes related to the trait in question. The Central Limit theorem merely shows how a normal curve arises from this model.

Now it may be that not all of those assumptions are satisfied. In particular, there may be genes whose effects are NOT additive — Downs Syndrome is one deviation from this model on the left tail. I’m not, though, aware of any such established deviation on the right side — there is nothing that corresponds to Gigantism in height, so far as I know.

And, so far as I know, the standard empirical finding for traits considered to be additive (excepting known genetic abnormalities), and measurable in a fully precise and non-controversial manner (unlike IQ or g), is that they follow a normal curve, well out into the tails. Height, as I had said, would seem to be a pretty good test case — though, again, there are some known genetic abnormalities that might be removed to assess the fit to the curve for the genes more correctly conceived of as additive.

My guess is that a test might be devised to determine whether IQ at the upper end really fits a normal curve. But even if in principle such a test might be devised and implemented, it will not come to pass, because the numbers are so scarce at this tail, the selection process so difficult, and the precise measurement of g so difficult, that it will be very hard to figure out whether such a deviation exists.

In the meantime, an assumption of a normal curve seems a very reasonable assumption; we should deviate from that assumption only if we have clear reasons to do so (discovery of non-additive genes of substantial effect would be one such).

I am curious about your financial analogy. Could you perhaps give an example of bets going wrong because they incorrectly assumed Gaussian?

I’m aware that there are good theoretical reasons to expect that traits like intelligence ought to follow a normal distribution, but that doesn’t necessarily mean they do. Please understand: I’m not arguing that intelligence is not normally distributed, I’m just trying to understand the basis for believing it is. Is this belief based purely on abstract theoretical considerations, like the Central Limit Theorem? Or are there more concrete reasons?

One motivation for my question is what has happened in the financial markets. People assumed, based on what they considered good theoretical reasons, that certain risks could be modeled by normal distributions, and they made huge bets based on that assumption. But as reasonable as that assumption was, in retrospect it’s looking like it might have been wrong. So how confident should we be that we are not also wrong about the way intelligence is distributed? In his post Razib noted the possibility that traits might have “fat tails.” What I’m wondering is to what degree fat (or thin?) tails would be obscured by the assumption of a normal distribution, and just how nonstandard a tail would have to be before we would be forced to notice that there was something wrong with our assumption.

Subregion-specific dendritic spine abnormalities in the hippocampus of Fmr1 KO mice, 2011

As I recall, I believe there have been some unreplicated findings in intelligence research with respect to a few snps connected to synaptic vesicles. It would seem reasonable that genes connected to synaptic plasticity would be connected to intelligence, but the results have not been confirmed.

Obviously, confirming dendritic phenotype in human subjects has not been easy, and there have been few volunteer participants for these projects.

don’t assume again, or i’ll ban you (again, i thought i’d banned you?). e.g.,

Would you say that the tail ends of the wealth bell curve directly reflects some sort of genetic “deservingness?”

i don’t agree that the extremely wealth are more genetically deserving. that’s what you get out of assuming someone’s views when left unstated, you shadow-box with strawmen of your own liking. DON’T DO THAT!

“Answer would be, I assume, that you think this line of argument means that we shouldn’t wonder at racial or sexual skews at the tail ends of social reward bell curves.”

Wondering is one thing, but resource and opportunity transferring from Asian and whites to blacks and latinos in the name of social justice and fairness is another.

Answer would be, I assume, that you think this line of argument means that we shouldn’t wonder at racial or sexual skews at the tail ends of social reward bell curves.

But, I think you will agree, long distance running is a massively oversimplified model if you are looking at much more general social outcomes.

For instance, practically everyone–say 99.9% of 7 billion–desires certain socio-economic outcomes–enough money to live comfortably, to make choices in ones life, to minimize the suffering on ones children etc. etc. Practically no one cares whether or not they are the world fastest marathon runner. It’d be nice, but it’s not what we’re here for.

So in terms of scale and stakes, the long-distance running as a metaphor obscures rather than elucidates.

Let’s look, rather, at the bell curve of the game a great many people are actually involved in and concerned about–making money.

Would you say that the tail ends of the wealth bell curve directly reflects some sort of genetic “deservingness?”

I’m skeptical. Why? Because economic rewards are doled out in a far, far more complicated fashion than, say, Boston Marathon winnings. If I want to win the Boston Marathon, what do I have to do? Run and do well in a qualifying race, over a set course of a particular distance with particular rules as to how to how to conduct oneself and a remarkably accurate timing method, thereby qualifying for Boston. Then I must run and win at Boston.

There are loads and loads of rules and technologies brought to bear that make marathons as pure a measurement of 26.2 mile running speed as we can make it.

If I want to destroy a company and get a 36 million dollar golden parachute, what do I need to do? Well, truth be told, there is no method by which anyone can do this. It is a privilege reserved for a few of us. How chosen? Well, that’s a complicated question. Orders of magnitude more complicated than the marathon question. And if you do not understand the process, you cannot possibly understand the meaning of the outcome, and relating the outcome to this gene or that becomes . . . meaningless.

I think that the presumption with regard to whatever it is that IQ is getting at — suppose it’s the g factor, or something highly correlated with the g factor — it should observe the same constraints that apply to any additive genetic trait. For reasons both theoretical and empirical, those traits, in the paradigm cases that we can accurately measure (such as height), do conform quite well to a normal curve, even toward the tails. If there’s a deviation from that curve, there would have to be special circumstances to explain it (i.e,, some significant non-additive feature that crops up at those tails). It’s likely that some of the left tail can be so explained (various kinds of genetic defects, many of which we already know), but not so likely, I think, that there are at the upper end (I don’t think there are known genes that engender great intelligence — one would think that such genes would have already swept through the population if there were).

All IQ tests are normed – i.e., their scoring is made to conform to normal distribution. A typical norming group has N ~ 1,000-2,000, so other than statistical deviations at the tails, distribution of IQ scores will always be normal. A reason to believe that such norming is a right thing to do is the Central Limit Theorem.

So do we have any good reason to believe that that assumption is even remotely right? For example, consider the possibility that “true intelligence” (whatever that might be) actually tails off according to a power law. Are our current test protocols good enough to rule this possibility out, or are we just assuming the possibility away by always fitting our results to a normal curve?