As an aside, the mistake in nutrition was simply that it wasn’t true. And it also wasn’t a “mistake,” it was a lie that the sugar industry paid to spread.
if you pick n numbers at random, it's not likely that one of them is bigger than the half of their sum.
but my intuition says that if you pick all variables from the same distribution, this should still hold.
At first, we don't know anything about the factors, so they are assigned a random importance. or am I missing something?
What's missing here are facts.
To dismiss something based on something anecdotally unrelated seems short-sighted.
A dominant factor can also only account for less than half of an explanation if there are enough factors. E.g. Peer group is 40%, parents are 30%, teachers are 20%, TV/videogames/groups-seen-but-not-interacting-directly-with 10%. Here peer groups would still be dominating but parents and teachers are significant factors as well. These percentages are close enough that it would be ridiculous to just focus on one (or even the first two alone).
I happen to believe peer groups are really important. But other things are important, too, including the adults.
Remove all the middle-aged and older men from a city, but still provide other necessities, and you'll see some terrible outcomes. (This is true in other species as well, like elephants where older males are hunted for tusks.)