In the mid-1980s I learned everything one needs to know in order to understand large organisations. I was in Aldershot, Britain’s biggest army town, having a pee in the toilet of a large pub patronised mainly by army squaddies. As I stood there relieving myself I noticed a graffito at eye level. “AT THIS MOMENT”, it read, “YOU ARE THE ONLY MAN IN THE BRITISH ARMY WHO KNOWS WHAT HE’S DOING.”

The ‘Peter Principle’ expresses this in slightly less charged language. In the late 1960s the Canadian psychologist Laurence J. Peter advanced the principle that “Every new member in a hierarchical organization climbs the hierarchy until he/she reaches his/her level of maximum incompetence”.

Now three physicists have found a way of simulating this effect using agent-based simulation methods. “Despite its apparent unreasonableness”, they write, “such a principle would realistically act in any organization where the way of promotion rewards the best members and where the competence at their new level in the hierarchical structure does not depend on the competence they had at the previous level, usually because the tasks of the levels are very different between each other”. Their simulations show that if the latter two features actually hold in a given model of an organization with a hierarchical structure, then not only is the Peter principle ununavoidable, but it yields in turn a significant reduction of the global efficiency of the organization.

So how to avoid it? The simulations suggest that in order to avoid such an effect the best ways for improving the efficiency of a given organization are (a) either to promote each time an agent at random or (b) to promote randomly the best and the worst members in terms of competence.

Hooray! At last I understand what’s been going on.