Back to my question about the distribution, if IQ is just a rarity ordering metric based on rarity, then IQ testing is somewhat confused. For example, say someone scoring 150 on an IQ test is rarer than someone scoring 160, they should be ranked higher according to your definition of the metric. If the claim in the article that higher IQs occur more frequently than predicted, then something like this scenario is possible and IQ scores may be unreliable as a rarity ordering metric.
At any rate, is there quantitative metric for intelligence?
Simplified view: people solve a test with a number of questions. They are getting ordered by how many questions they get right.
Tests are constructed to produce Gaussian distribution of numbers of correct answers. Some questions are easy, almost everybody can solve them. Some questions are difficult, almost nobody can solve them. There should be progressively less and less people getting more questions right.
But in reality, it's not a perfect Gaussian distribution. There are some numbers of questions that have more people getting them right than would be predicted by normal distribution.
Now, about quantitativeness. We could get somehow quantitative metric, if questions would simple and uniform in structure, for example test composed just of "how fast you can multiply x-digit numbers" task, or test solely composed of "how fast you can arrange pieces into a particular shape" task.
But it's not like this. There are different tests, some of which have several thematically different sections. Even inside one section, questions do differ a lot (for example, some shapes are harder to compose of primitive elements, how would you quantify this difficulty?).
To further complicate matters, usually completely different tests are used for different intelligence ranges.
And we are not even speaking about normalizations. Your rank is computed just for your age group. For the same raw score, you get extra points if you are younger or older than the optimal age.
If I remember well, there is a fast ramp up of raw scores till 18 years, followed by a slow decline afterwards (rate of decline is slower for more intelligent people).
And then there are national/race differences. And Flynn effect. It's much more messy than it looks.
At any rate, is there quantitative metric for intelligence?