In physical science the first essential step in the direction of learning any subject is to find principles of numerical reckoning and practicable methods for measuring some quality connected with it. I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the state of Science, whatever the matter may be.
-- Lord Kelvin
If you believe that science is about describing things mathematically, you can fall into a strange sort of trap where you come up with some numerical quantity, discover interesting facts about it, use it to analyze real-world situations - but never actually get around to measuring it. I call such things "theoretical quantities" or "fake numbers", as opposed to "measurable quantities" or "true numbers".
An example of a "true number" is mass. We can measure the mass of a person or a car, and we use these values in engineering all the time. An example of a "fake number" is utility. I've never seen a concrete utility value used anywhere, though I always hear about nice mathematical laws that it must obey.
The difference is not just about units of measurement. In economics you can see fake numbers happily coexisting with true numbers using the same units. Price is a true number measured in dollars, and you see concrete values and graphs everywhere. "Consumer surplus" is also measured in dollars, but good luck calculating the consumer surplus of a single cheeseburger, never mind drawing a graph of aggregate consumer surplus for the US! If you ask five economists to calculate it, you'll get five different indirect estimates, and it's not obvious that there's a true number to be measured in the first place.
Another example of a fake number is "complexity" or "maintainability" in software engineering. Sure, people have proposed different methods of measuring it. But if they were measuring a true number, I'd expect them to agree to the 3rd decimal place, which they don't :-) The existence of multiple measuring methods that give the same result is one of the differences between a true number and a fake one. Another sign is what happens when two of these methods disagree: do people say that they're both equally valid, or do they insist that one must be wrong and try to find the error?
It's certainly possible to improve something without measuring it. You can learn to play the piano pretty well without quantifying your progress. But we should probably try harder to find measurable components of "intelligence", "rationality", "productivity" and other such things, because we'd be better at improving them if we had true numbers in our hands.
By more predictable, I meant greater accuracy in predicting, not that less computing power is required to predict. Someone who performs well on tests is perfectly predictable: they always get the right answer. Someone with poor performance can't be any more predictable than that, and is often less.
Just because the bug model has some value doesn't mean that the error model has none. I would be surprised if a poorly performing student, given a test twice, were to give exactly the same wrong answers both times. I don't understand you claim that people with worse performance would be more predictable. Given that someone is a good performer, all you need to do is solve the problem yourself, and assuming you did it correctly, you now know how that person would answer. To predict the worse performer, the move history is woefully inadequate. Poor performance is deterministic like a dice throw is deterministic. You need to know what their bugs are, what the exact conditions are, and how they're approaching the problem. Someone who is using math will correctly evaluate 5(2+8) regardless of whether they find 2+8 first and then multiply by 5, or find 52 and 58 and add them together. But someone who doesn't understand math will likely not only get the wrong answer, but get a different wrong answer depending on how they do the problem. Or just give up and give a random number. Just knowing how they did the problem before doesn't tell you how they will do that exact problem in the future, and it certainly doesn't allow you to extrapolate how they will do on other problems. If someone is doing math correctly, it doesn't matter how they are implementing the math. But if they are doing it incorrectly, there are lots of different ways they can be doing it correctly, and given any particular problem, there are different wrong ways that get the same answer on that problem, but different answers on different problems. So just knowing what they got on one problem doesn't distinguish between different wrong implementations.
Learning poorly from your environment does not mean not updating, it means that you are updating poorly. Given the problem "d = rt, d = 20, r = 5", if you tell a poor learner that the correct procedure is to divide 20 by 5 and get t = 4, then given the problem "d = rt, r = 6, t = 2", they will likely divide 6 by 2 and get d = 3. They have observed that "divide the first number by the second one" is the correct procedure in one case, and incorrectly updated the prior on "always divide the first number by the second one". To know what rule they've "learned", you have to know what cases they've previously seen.
Good learners don't learn rules by Bayesian updating. They don't learn "if you're given d and r, you get t by dividing" by mindlessly observing instances and updating every time it gives the right answer. They learn it by understanding it. To know what rule a good learner has learned, you just need to know the correct rule; you don't need to know what cases they're seen.
That there are some cases where idiots can screw things up more than selfish people is rather self-evident. "Can" does not border on "necessarily will". Intelligence doesn't lead to goodness in the sense of more desire to do good, but it does generally lead to goodness in the sense of more good being done.
The whole point of an alliance is that you're supposed to work together towards a common goal. If you're trying to find stupid people so that you can have the upper hand in your dealings with them, that suggests that this isn't really an "alliance".