Question: In purest form the Peter Principle seems to imply two special features of a promotional system:
(a) once reaching a level of incompetence an individual never again will be competent, and
(b) an incompetent person is never promoted. Show that, in the case where the promotion and recycling matrices are constant, these two assumptions Imply that the distribution of competents and incompetents is the same at every level except the first.