1) What is the Peter Principle?
"Everyone rises to their level of incompetence"
or: people get promoted when they are competent, up to the point where they are no longer competent in their job, then they rise no further.
This sounds rather self-evident, but it took until 1969 for it to be formulated, by psychologist Laurence Peter. There are corollaries: that, over time, every post gets filled by an incompetent, and that the real work is done by those who haven't yet arrived at their level of incompetence.
Of course, it was humorous, but undoubtedly gained so much traction because there seemed to be rather more than a grain of truth in it. You can read more about it in the Wikipedia article.
2) The surprising outcome of a scientific study
New Scientist (19-Dec-09) reported studies that came to some unexpected solutions. Stanford's Edward Lazear's modelling suggested people have a baseline competence which is enhanced by some circumstantial factor to the point they perform a particular task (or project) "unusually well". Once they're promoted, that circumstance is gone, and they fall back to their baseline (lesser) competence level.
Further modelling by Alessandro Pluchino et al examined whether ability at one level was a predicator of ability at a higher level. They found it was not so: in fact, promoting the best performers merely removed people from successful position fits. Promotion ended, and the Peter Principle is demonstrated, "locking incompetence in place". On the other hand, promoting poor performers at least removes them from unsuccessful work situations. They thus suggest the best strategy seems to be to:
promote people at random
3) The Simmonds Solution
At the risk of stating the obvious (which, it must be said, Laurence Peter did, to great acclaim), I suggest the solution is to:
Rotate non-stellar performers into higher positions,
then choose the best for permanent advancement
That way, you'd keep good performers in good positions (and could reward them accordingly), while testing the options for moving people into positions that may suit them better.
Admittedly, rotation is also suggested in the New Scientist article. But I claim provenance with my provisos: that high-performers are excluded from rotation (with appropriate recompense), and that permanent promotion should be the outcome of a successful rotation exercise - without obliging that the position be filled by the best less-than-competent person.
Obvious, isn't it? - once spelt out. Still, if nobody else has articulated this exact solution, I claim naming rights.