One summary of the Peter Principle, named after psychologist Laurence J. Peters, is that “in a hierarchy every employee tends to rise to their level of incompetence.” Three Italian physicists—Pluchino, Rapisarda, and Garofalo—claim to have put proof to this puzzling problem. Today, we examine their paper, which is making the rounds, and has even won an Ig Nobel!
Peter’s perplexing promotional principal runs like this: a vacancy in an organization appears, and somebody in that organization who had heretofore labored somewhere in the lower ranks is elevated to a new eminence.
Peter assumes that when people are promoted they will not be as good at their new jobs as they were at their old jobs. This presumes two conditions. One, as is reasonable, new jobs are different; and two, that just because somebody was efficient at their old job it does not imply that they will be efficient at their new job. It isn’t necessary that the new job be “harder” on some mysterious global scale, just different from the old one.
It is difficult to discuss the Peter Principal (PP) because one has to be careful to make testable statements that can be shown to have been derived from the PP. In one reading, the PP does not imply that every boss is incompetent: not every boss is promoted from below within an organization, for example. But in a global reading, the PP can be used to imply that everybody is at least somewhat incompetent. After all, everybody at whatever level was promoted from below at some point! (Consider also the people who are line workers, who are never promoted.) That everybody works at their “level of incompetence” is obviously false, and it shows that the PP, if true, cannot be a global phenomenon.
Pluchino, Rapisarda, and Garofalo
Never mind if you don’t understand that (fatal?) objection. Let’s look at how Pluchino and his brother physicists handled the problem.
The simulated a hierarchical company with six levels, the bottom being filled with 81 lackeys (perhaps peons is better word), the pinnacle being manned by one soul. Slots in the company go vacant for two reasons: when somebody turns 60 they are mercilessly turned into the street; and they are fired if their “competence” falls below a score of 4. The simulation runs one “year” at a time.
Each employee is started with a competence, which (they say) runs from 1 to 10; higher is better. The level is chosen by simulating numbers from a normal distribution with a central parameter of 7 and a spread of 2 (the “mean” and “standard deviation”). Now, right away you might notice a significant problem. Competence, in their simulation, is a number from 1 to 10. But the probability of simulating a competence (with that normal) below 4 is 6.7%, which is the same probability of simulating a competence greater than 10.
Presumably—the authors do not say—when a person’s competence soars about 10, it is truncated back to that level. But—and here is the key—when a person’s competence sinks below 4, they are canned.
Now, when a person is promoted (because a slot above them has opened) that person’s competence for the new job has to be calculated. The authors do so in two ways:
- Common Sense: the employee’s new competence is equal to the old plus a uniform random variable from -1 to 1. This has the effect of inducing a strong correlation between the old and new competencies. Since I do not know how the authors handled the truncation problem mentioned above, I cannot calculate this correlation exactly. But it is at least 90%! The authors might be aware of this, but they never mention it.
- Peter Principle A person’s competence is re-simulated from that same normal distribution. Here, the correlation between a person’s old and new competence is 0. This, of course, is not plausible for real situations. However, it is a useful baseline to compare against. But again, the authors do not appear to have noticed this correlation (I may do them a disservice; they might have noticed it but thought it so obvious, that it was not worth commenting on).
At this point, it becomes complicated. Suppose a person has a competence of 4.9 and there competence upon promoted is calculated under common sense. It is then possible that they immediately fall below a competence of 4 (just in case the uniform random variable is -0.9 or smaller). Are they then immediately fired? That is, they are promoted then immediately fired. It is of course even worse for those whose competencies upon promotion are recalcuated under the PP. If, say, a person had a competence of 10, when they are promoted they have a 6.7% chance of dropping below 4 and being fired!
The authors do not say how they handle this, but the evidence of their Figure 2 (explained in a moment) suggests that they immediately fired after promotion.
How well does the organization operate under these rules? Some measure of global efficiency must be calculated. The authors summed “the competences of the members level by level, multiplied by a
level-dependent factor of responsibility”. They normalize the result by its maximum possible value (when everybody had a competence of 10). Of course, higher is better.
We still have to consider how to promote a person. One idea is to look to the level just below the level which has an open position and then promoting the Best, i.e. the person with the highest competency. Another is to promote the Worst, i.e. the person with the lowest competency. Finally, to promote one at Random.
There are thus six scenarios: two levels of simulating competence by three ways of promoting. Which of these six is best in the sense of leading to the highest global efficiency. Look at their Figure 2 (an average of global efficiency over many runs) to see:
It’s promoting the worst! Coupled, of course, with a competence generated by the (unrealistic) PP.
The reason, I think, is simple. When the worst person is promoted they have a pretty significant chance of having their new competence falling below 4 and thus being fired. A new person then has to take their spot; chances are this new person will have a new competence much higher. To fix the idea, suppose the person being promoted has a competence of 4.1. Upon promotion, this person has a 93.6% chance of having a higher competence! But if they have a worse, they will be fired, and the new person also has a 93.6% of having a higher competence.
That is, the author’s main finding is an artifact of how they did the simulations.
The line on Fig. 2 indicating the “second best” strategy is promoting the best and having a new competence generated by common sense, i.e. the highly correlated competence. Notice that it is just about 6.7%/2 points below the “best” strategy. We already know where the e 6.7% comes from; the 2 is from the chance of the uniform random number being negative.
The authors do go on to say that if we do not know how competency is “transfered”, a random promotion strategy has some benefits. But Peter Principle competency transference is extremely unrealistic. Bosses do not just promote based on how competent somebody was in their old job: they also estimate how well they think they will do at the new one. All evidence suggests that there must be some (positive) correlation between a person’s old and new competence.
This analysis does not prove that the PP is wrong, but it does say that, for the type of organization envisioned by Pluchino et al., common sense has not been overthrown.
Thanks to the several readers who asked I take a look at this paper.