William M. Briggs

Statistician to the Stars!

Peter Principle Particulars: Pluchino Paper Perused

Introduction

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:

  1. 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.
  2. 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.

Global efficiency

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:

Pluchino et al Figure 2

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.

Conclusion

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.

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Thanks to the several readers who asked I take a look at this paper.

12 Comments

  1. A fine example of recreational computing. I’ve done this sort of thing myself. I’d never dream of publishing it and calling it ‘research’, though. I hope they did it in their own time.

  2. My brain is bossy. It rose to its current level from the ranks having started as a lowly zygote. Further promotion is unlikely unless it promotes itself — a clear sign of incompetence.

  3. “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.”

    You’re assuming a competent boss. It would be interesting to run a simulation where the change to the competence of the promoted is dependent on the boss doing the promotion. Lower boss competence would yield a higher range (+/- (10 – boss)) or simply a larger downside. My guess is that poor bosses tend towards Peter Principle, competent bosses tend toward common sense. And maybe an incompetent CEO yields a sharp decline in overall company competence.

  4. Promotion decisions and succession in hierarchical organizations are areas of long term interest.

    Some thoughts from 30 years working on promotion and succession type issues.

    Promotion decisions frequently lead to an exodus of those who considered themselves qualified candidates for the promotion but did not receive it. This can lead to a major leaking of talent. The less variance there is in the talents of the candidates for promotion, the greater the potential for losses in organizational effectiveness. (Think of the carnage that results when all the alphas are close in strength.) Government bureacracies tend to not experience an exodus to the same degree – the pensions and security are too good to give up. Instead, the disgruntled candidates work to undermine the effectiveness of the “perceived illegitimate”promotee and is a major source of bureaucratic infighting. (This also occurs in non-Governmental hierarchies especially when the losers believe that their new boss will not be around for long or does not have the power to fire them. (In the Ottoman Empire, this potential dynamic led to the slaughtering of all potential claimants to the Empire, i.e., younger brothers and their children, thereby leading to another and more permanent leaking of talent.)
    The net result is that promotion decisions that are perceived as illegitimate by many result in overall losses of organizational effectiveness.

    Many promotions are made by selecting individuals from outside of an organization. This typically lengthens the time it takes to recognize that the new person is not as competent as one originally assumed. The immediate leakage of talent might be less, but other forms of organizational sabotage and “withholding” of competence are probably the same.

    Many organizations have two or more promotion tracks: Rank in job and Rank in Person. University academic promotions tend to be the latter. Government bureaucracies certainly have both and they are notoriously inefficient. The PP is designed to apply to the former but can also apply to the latter when objective measures of accomplishment are not used.

    Not all incompetent “promotees” get fired or visibly fail before they get promoted a second time. This can lead to some spectacular failures. Military History provides numerous examples of such incompetents.

    The firing of incompetents is much, much lower than Pluchino et al’s model assumes. As academics they should know this.

    (If anyone is interested in a more formal analysis of these issues, Harrison White, many years ago, wrote a seminal book on this issue called “Chains of Opportunity” which involved the use of Markov Chains and block modelling. My sense is that it led to the development of the tools that are now part of Social Networking Analysis.)

  5. It’s generally easy to predict who will get promoted, and in general a number of themes apply, with certain also predictable exceptions:

    – “Like me good, not like me bad” — most bosses will endorse most strongly those that view things as they do.

    – Psychological health: “A” people hire/promote other “A” people; “B” people hire/promote “C” people etc. In words this means that people with a healthy self confidence & lack of significant neurotic traits will readily seek out & hire people that are as competent or of greater competence than they are.

    – Many organizations at the lower levels demand a particular skill set that rapidly becomes irrelevant at higher levels (e.g. a great cop/detective will generally make a lousy manager–especially where political skills are mandated — a great example of how bad this can be is the FBI’s mismanagement of its Virtual Case File software development [complete & total failure]). Thus, promoting based on top performance to & beyond certain levels is a bad approach–unless the relevant skills are being evaluated (and experience in the lower levels is very often a strong benefit, though exceptional competence is not necessarily [i.e. a mediocre soldier may make the most proficient general] — very counterintuitive for many to grasp). In most organizations the wrong skills are weighted heavily if not totally (union practices are usually good examples of such bad examples — institutionalized seniority over competency, for example).

    AS FOR: ” Bosses … promote based …. also estimate how well they think they [the promotee] will do at the new one.”

    BAH HUMBUG, at least in many situations. I think is was Mackay [author of “Swim with the Sharks,…” (if not him some other competent management consultant) that noted that his view was that any senior manager/CEO’s recommendations for replacement be rejected sight-unseen. Reason: they tend, much much more often than not, to recommend people that will make them look good in history…which is bad for the company’s prospects.

  6. Promoting the worst under the unrealistic PP assumption — No duh!

    The system takes the least competent employee and gives them a do-over in calculating their competency. It is bound to raise their number. And, if it doesn’t, it will get them fired, and move another incompetent up the management chain, where they can again re-roll their competency…

    On the Peter principle in general — not all managers are incompetent. Many are good and await the opportunity to move to the next step in the chain of management. Eventually, they will stop rising. The CEO is not necessarily incompetent. Of course, still could be. His direct reports are also not necessarily incompetent, either. Direct reports are merely less competent than the CEO was at the time he was promoted. Middle management will have the highest quotient of people who have “maxed out.”

  7. I always thought the peter principle meant something slightly different. You don’t promote people who are competent at their job because they are making you money by getting their job done.

  8. I believe the premise of the Peter Principle is that a worker gets promoted for doing a good job in the current position. Success in the new position leads to further promotion. The process continues until the employee reaches a position where he cannot function competently whereupon he ceases to get further promotions. Thus he has risen to his level of incompetence, Everyone my age can cite at least one real life example. Fortunately, there are exceptions.

  9. brad tittle

    That’s a different principle.

    http://en.wikipedia.org/wiki/The_Dilbert_Principle

  10. Since we never know who has reached their maximum level until AFTER they retire or die, it is much harder to gather hard data.

  11. ExGovernment Pat

    16 October 2010 at 1:32 am

    0 to 10……..the actually really competent people are about 11 and have left your organization out of frustration. One of the major problems with State and Federal government positions involving scientists, like the EPA or state environmental agencies, is that in order to get a pay raise you must govern more people. This pay scale scheme requires that good scientists often end up as bad managers. Good scientists do not often have the managerial skills needed to run a work group. They are trained as scientists, not managers.

  12. As one who spent 15 years in management in a major aerospace company in California, the application of PP to promotions is interesting. I remember on several occasions some of us felt that Peter was an optimist. Promotions were seemly based on other criteria that competence. In fact if one examines salary curves from just about any major commercial institution, not necessarily aerospace, you see wage increases that quickly( less than 10 years) asymptote to a ceiling within a given job rating in both the labor force and in management. New hires will have a higher wage ceiling than the current wage earners. Thus to get more money the workers need to seek a promotion to a higher classification whether they are competent or not.
    What do these wage curves tell us? They suggest that the corporation believes that employees become less and less competent to perform within their job classification with time and only by hiring new employees at a higher starting wage can they maintain their technological edge. However, they are willing reclassify them, (promote them) to a higher level despite the fact that the rate of increase in wage or salary reflects a belief that they are not as competent as they were previously. I suspect that this paradox does not explain why the PP works but reflects corporation accountants who see wage and salaries as costs and not benefits to the corporation. Hiring new employees at lower wages and salaries than the average employee saves money in the short term. What do you think?

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