Mitchell, I think the No Free Lunch theorems of Wolpert and Macready imply that if you take two EUMs and average their results over all possible problems, the two will be necessarily indistinguishable. So your measure of intelligence would imply that unequal general intelligence is impossible.
Of course, you could probably rescue your definition by not including all possible problems, but only realistic ones. In other words, the reason it is possible to derive the NFL theorems is because you can invent a theoretical world where every attempt to accomplish something in a reasonable manner fails, while every unreasonable attempt succeeds. With more realistic limitations on the set of possible problems, you should be able to define general intelligence in the way stated.
If you sum over an infinite number of worlds and weight them using a reasonable simplicity measure (like description length), this shouldn’t be a problem.
Mitchell, I think the No Free Lunch theorems of Wolpert and Macready imply that if you take two EUMs and average their results over all possible problems, the two will be necessarily indistinguishable. So your measure of intelligence would imply that unequal general intelligence is impossible.
Of course, you could probably rescue your definition by not including all possible problems, but only realistic ones. In other words, the reason it is possible to derive the NFL theorems is because you can invent a theoretical world where every attempt to accomplish something in a reasonable manner fails, while every unreasonable attempt succeeds. With more realistic limitations on the set of possible problems, you should be able to define general intelligence in the way stated.
If you sum over an infinite number of worlds and weight them using a reasonable simplicity measure (like description length), this shouldn’t be a problem.