Presumably, we're looking at some form of ephebeocracy that puts a younger child theoretically in charge to make a point, but actual power is held by teens and twentysomethings?Well, the simple fact remains that any state relies on force to enforce its will. Adults will defeat kids in any fight. Ergo, there have to be adults using the system for their own ends and thus enforcing it for their own ends.
Or we're looking at something like Timothy Zahn's A Coming of Age, but where the adults don't regain control after the first generation complete puberty and lose their powers.