The Peter Principle
states that "in a hierarchy every employee tends to rise to his level of incompetence", meaning that employees tend to be promoted until they reach a position at which they cannot work competently. It was formulated by Dr. Laurence J. Peter and Raymond Hull in their 1969 book The Peter Principle, a humorous  treatise which also introduced the "salutary science of hierarchiology."
The principle holds that in a hierarchy, members are promoted so long as they work competently. Eventually they are promoted to a position at which they are no longer competent (their "level of incompetence"), and there they remain, being unable to earn further promotions. Peter's Corollary states that "in time, every post tends to be occupied by an employee who is incompetent to carry out their duties" and adds that "work is accomplished by those employees who have not yet reached their level of incompetence". "Managing upward" is the concept of a subordinate finding ways to subtly "manage" superiors in order to limit the damage that they end up doing.
This principle can be modelled and has theoretical validity for simulations. However, all of the real-world evidence for it is anecdotal (and often intended to be humorous in nature).