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This paper identifies two possibilities for someone’s competence after a promotion: the Peter Principle – i.e. the competence after promotion is uncorrelated to the old competence – and the common sense approach – i.e. the competence after promotion is highly correlated to the old competence. Now you can run organizational simulations with different promotion rules: Promote the best, promote the worst, promote at random, promote either the best or worst at random.

As you might expect, promoting the best works well if future competence is correlated to past competence. Promoting the worst works best if future competence is uncorrelated with past competence. Promoting at random works no matter what the correlation really is, and promoting the best or worst can be made to produce the same overall outcome no matter what the future competence rule is.

I find this rather disquieting when you try and map this into real organizations. Could you really do promotions on a random basis ?

If there is an easy way to measure employee performance then the answer is no, random promotions are not possible. If employee X made 10 widgets in a year and employee Y made 20 widgets then X might have grounds to sue the company if Y was promoted instead.

However, it is rarely the case that things are so easy to measure. So-called "soft skills" such as communication and the ability (or willingness) to manage staff will often give organisations the additional leeway to promote a person who probably isn't actually very good at what they do. Sometimes (often?) this decision will be made because political alliances have been made. Other times it may be to fill a racial or sexual quota.

These additional factors probably introduce a good deal of randomness into the mix when measured over time and averaged over all appointments.