How would that happen? Well, the authors argue it should be expected in any organization where the following two conditions hold:

1. The best member are rewarded with promotions
2. Competence in a new position is not highly correlated with competence at a prior level

The authors simulated the preceding in a pyramidal organizational form using a mathematical agent model. Here is the outcome:

Here we show, by means of agent based simulations, that if the [above two conditions] actually hold in a given model of an organization with a hierarchical structure, then not only the "Peter principle" is unavoidable, but it yields in turn a significant reduction of the global efficiency of the organization. [Emphasis mine]

Granted, this shouldn't be surprising news, one would think, to anyone who has spent any time around large organizations. A disproportionate number of the positions always seem filled by people who elicit a WTF? reaction from reasonable-minded observers.

So, do we just live with it? After all, we can hardly get around elevating the best people, and it isn't unreasonable to think that one's experience in a former position doesn't adequately prepare for the new one.

Not necessarily, according to the authors:

...the best strategies to improve, or at least not to diminish, the efficiency of an organization, when one ignores the actual way of competence transmission, are those of promoting an agent at random or of randomly alternating the promotion of the best and the worst members. We think that these results could be useful to guide the management of large real hierarchical systems of different nature and in different fields.

Whoa, it turns out calling someone's promotion "random" is a compliment. Who knew darts could be so handy at promotion time?