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The Peter Principle and the limits of our current understanding of organizational incompetence



This article discusses the implications of the Peter Principle, as it reflects the intriguing reality of the most organizational systems. Deliberately or not, the latter frequently encourage individuals to climb to their level of incompetence ending up in a situation in which most job positions are occupied by employees incapable of carrying out their duties, and leaving the few remaining ones to actually accomplish organizational goals. The article contains a comprehensive analysis of previous research and, based on these findings, develops several research directions which would bring to light new insights for the effectiveness of organizations and their HR strategies.
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The Peter Principle and the limits of
our current understanding of
organizational incompetence
This article discusses the implications of the Peter Principle, as it reflects the
intriguing reality of the most organizational systems. Deliberately or not, the
latter frequently encourage individuals to climb to their level of incompetence
ending up in a situation in which most job positions are occupied by
employees incapable of carrying out their duties, and leaving the few
remaining ones to actually accomplish organizational goals. The article
contains a comprehensive analysis of previous research and, based on these
findings, develops several research directions which would bring to light new
insights for the effectiveness of organizations and their HR strategies.
Peter Principle; performance evaluation; promotion; incompetence; organizational
1. Introduction
Incompetence defies the barriers of time or place. People come across it
during their entire lives, and feel its effects every day, in various forms,
and with a tremendous impact on their activity, career and personal
development. In organizations, incompetent people occupying decision-
making positions are even more harmful. Given the direct connection
between the success or failure of an organization and the caliber of its
employees, without the right person in the right place, organizations
cannot sustainably progress and prosper. In other words, decisions about
placing people are critical because they determine the performance of the
entire organization (Drucker, 1998). If, by any mistake, a considerable
number of employees eventually reach their level of incompetence, few
remain to be effective and productive (Peter and Hull, 1969). However,
even in this scenario, a company may survive due to the sufficient good
decisions made by the right people who will compensate the mistakes or
lack of action of the incompetent ones.
This solution is only suitable in the short run, whereas in the long run it
will negatively affect the welfare of the company. The explanation resides
in the employees’ operational conditioning. Employees tend to improve
their own activity when they see others being rewarded. Yet, when
rewards go to non-performance, flattery or mere cleverness, Peter
Principle is going to emerge and the organization risks developing a
culture of incompetence (Drucker, 1998). In this case, incompetent people
prevail, and the competent ones will eventually leave hindering the
company’s growth.
Now part of the business world lexicon, Peter Principle is oftentimes used
to ridicule those aspiring for promotions out of the job that they are
(over)qualified for until they reach the one exceeding their level of
competence, or those who have been on the executive seats for a long
Ghinea Valentina Mihaela
The Bucharest University of
Economic Studies
UNESCO for Business Administration
010731, Bucharest
Cantaragiu Ramona
The Bucharest University of
Economic Studies
UNESCO for Business Administration
010731, Bucharest
Ghinea Mihalache
University Politehnica of Bucharest
Machines and Manufacturing
060042, Bucharest
2 Proceedings of 2100 Projects Association Joint Conferences 5 (2016) X-X
time (Peter and Hull, 1969; Faria, 2000). Since it refers to the rampant incompetence found everywhere, not
only in business, Peter Principle continues to fascinate both scholars and practitioners. As any organization
could end up at a certain point with incompetent leaders and losing its best individual performers, the issues
raised by the Peter Principle remain just as true nowadays as in 1969, when the theory was conceived.
Exploring the issues that lead to the manifestation of the Peter Principle in organizations is useful for creating
strategies to avoid them and warning system to detect them, thus leading to improved HR practices.
2. Description of the Peter Principle
Promotions are essential for a hierarchical organization, as they play both as incentive and enhancer of
organization efficiency and performance by assigning employees to the jobs that best suit their abilities
(Milgrom and Roberts, 1992). Theoretically, firms initially place individuals in jobs where they can do little
harm, and those who prove able are then promoted to positions that require a higher level of ability. This
approach is the core of the tournament model (Lazear and Rosen, 1981), which explains the positive effect that
promotion and an associated increase of wage has on employees. The employee is generally motivated to exert
effort and take actions beneficial for the organization. However, this conventional view is increasingly called
into question, as it has been observed that promotions, if not wisely managed, could also have a negative
impact as well.
2.1. Defining Peter Principle
In 1969, Peter and Hull advanced an apparently paradoxical principle summarized as follows: “Every new
member in a hierarchical organization climbs the hierarchy until he reaches his level of incompetence” (Peter
and Hull, 1969, p. 34). It is generally agreed that, in a hierarchy, promotion is strongly connected to the work
competently done. However, the Peter Principle highlights serious flaws in the classical promotion theory, and
it even contradicts the conventional view that it acts as a major source of incentives.
The theory sustains that, sooner or later, employees will be promoted to a position for which they will be no
longer competent, as the competence necessary for the new level could be uncorrelated to that required by
the previous one. Thus, employees fall into (un)conscious incompetence or even deliberate incompetence
(requiring supplementary payment for seriously working). The upward process eventually stops, and there is no
downward process since bureaucracy makes it very difficult to demote an employee, even if that person would
much better fit in a lower job. It is not surprising then that most of the higher levels end up being filled by inept
people simply promoted because they were good at different tasks before promotion. Moreover, this
phenomenon is not limited in scope, since it could happen to any employee at any level in the hierarchy, be it
business, industry, trade-unions, politics, government, armed forces, religion, or education (Peter and Hull,
1969). Nevertheless, it should be made clear that the Peter Principle is not a law (Schaap and Ogulinck, 2011),
but only a generalized principle, explaining a general tendency. The basic idea is that a new job requires a
different set of skills in which the employee did not previously excel and which he usually does not possess.
2.2. Dealing with Peter Principle
There are various processes and characteristics of organization which help the Peter Principle emerge. Out of
these, we only mention a few of them, namely hierarchical exfoliation, paternal in-step, and the political nature
of organizations. If the first one describes how organizations rid themselves of both the least and the most
competent employees (as all of them are objectionable), the second one brings into discussion how a family
member is suddenly promoted several steps above his level of competence (Peter and Hull, 1969). Moreover,
politics usually interferes with the reward and promotion organizational practices and thus real competence is
neglected and the pay-back promotions achieved (Beeman, 1981).
Dealing with Peter Principle is difficult because there are employees who never realize that, one way or
another, they have reached their level of incompetence. They are “perpetually busy”, “never lose their
expectation of further promotion”, and “remain happy and healthy while joking instead of seriously analyzing
things. Fundamentally, this could be seen as an act of substitution in which the employee replaces real work
with other tasks that he is able to carry out. In extreme cases, an employee reaching his level of incompetence
can no longer do any useful work. He is overly stressed, mentally disturbed and frequently sick. Final placement
syndrome is a term describing this situation, and displays a variety of behavioral and psychological clues
Proceedings of 2100 Projects Association Join Conferences 5 (2016) X-X 3
pointing it out (Peter and Hull, 1969): a) fonofilia (need to use several means of communication to keep close
contact with colleagues and subordinates); b) papyrophobia or papiromania (having a clean desk to give the
impression of efficiency or keeping the desk full to give the impression of too much work); c) clasofilia (mania
for the classification of work documents of fear of not losing them); d) tabag gigantism (obsession with having
the biggest office); e) tabulophobia (excluding work desks from the office); f) self-pity (based on previous
experiences of competence); f) rigor cartis (abnormal and inflexible preoccupation for elaborating
organizational charts, graphs and diagrams); g) unpredictability (as a defensive attitude to hide incompetence)
and irrational prejudices related to employees’ appearance; h) Coupp syndrome (hiding the inability to make
decisions behind a democratic decision making process); and i) structurophilia (excessive preoccupation for
building instead of for the work that should be done).
Considering the cascade effect that the manifestation of Peter Principle could trigger within an organization,
some techniques were thought of for dealing with employees who have reached their level of incompetence.
Percussive sublimation is a pseudo-promotion technique used to hide the flaws in the organization’s promotion
policy. It consists of promoting an incompetent employee to a higher position where he has no new
responsibility in order to enable a more competent employee to step into the previous position. This supports
staff morale and maintains the hierarchy. Reversely, firing the incompetent person might result in him getting a
job with a competitor where, despite his incompetence, his knowledge could be dangerous. Another pseudo-
promotion is lateral arabesque which refers to giving the incompetent employee the impression of a
promotion through a more impressive title and then moving his office outside the principal working area,
without an actual increase in rank or in pay (Peter and Hull, 1969).
3. Previous studies on Peter Principle
There are scholars who agree with the validity of Peter Principle, and there are also others contesting it. The
former are keen on finding explanations that support their point of view and examples confirming it, whereas
the latter look for evidence proving that nothing abnormal is happening. In between these extremes, there are
others not focused on the frequency of occurrence or the degree of accuracy of the Peter Principle, but rather
on finding methods to avoid and/or alleviate incompetence within organizations.
a. Organizational hiring and promotion practices within organizations foster incompetence
The way in which employee competence is judged by superiors depends on the level of competence of the
latter (Peter and Hull, 1969). If these superiors are still at a level of competence, they will evaluate
subordinates in terms of the performance of useful work. If the contrary, they will probably rate subordinates in
terms of institutional values (i.e. supporting rules, rituals, and forms of the status quo). Bernhardt (1995) and
Faria (2000) argued that even if promotion is based on the good performance of one task, the skills required by
a new one may be quite different. This can lead to the appearance of the Peter Principle as Kane (1970) found
that it is unlikely for an employee who has been promoted to perform as well as on his former position, since
he has new tasks and responsibilities, and much of his experience is of little help. Moreover, once arrived at a
position for which he is no longer competent, the employee is unlikely to be demoted because the employer is
aware of the need to pay a bonus to retain a demoted worker (Bernhardt, 1995). Aside, Acosta (2010) showed
that the opportunity for future promotion is strongly negatively related to the frequency of prior promotions
and that incumbent employees are disadvantaged in comparison to externals.
In 2007, Baleanu highlighted the existence of certain groups within the organization that compete for limited
resources and constantly bargain for the fulfillment of their group’s desired goal. By utilizing the push and pull
method advocated by Peter and Hull (1969), employees are able to meet the goals of their group, while
attempting to fulfill the overall objectives of the organization. The end result is that a worker is promoted to
levels where his decision making more strongly serves the group, than the larger organizational objectives, and
thus the employee appears incompetent. Moreover, Fairburn and Malcomson (2000) showed that motivating
an individual to perform well in a certain position by promising a promotion might result in a transfer to
another position for which the person is not suited, and that employees can sway performance evaluations
with bribes (collude with their supervisors to extract higher wages with no additional effort), which makes
promotions based on evaluations biased. On the other hand, by making workers’ earnings contingent on their
job, and managers’ pay contingent on the firm’s profits, managers’ interests become closely related to those of
4 Proceedings of 2100 Projects Association Joint Conferences 5 (2016) X-X
the owners. Therefore, even in cases of organizations reputed for honest behavior, Peter Principle may have a
sound basis unless incentives for promotion are not tied directly to managers’ incentive programs.
b. Incompetence is only a temporary/relative state or the result of psychological stress
Patz (1975) researched on the idea that employees have a beginning ability potential, an upper limit (ceiling),
and that their ability develops at a rate proportional to the difference between the ability ceiling and the
current level. Besides, the ability ceiling itself rises at a rate proportional to the rate of change in ability and,
that, given the cyclical nature of ability development, it is possible to simply wait until an employee begins to
reassert a level of ability matching the demands upon him. A different approach had Hess (1976). He related
incompetence to a certain level of anxiety and depression arising from childhood conditioning which teaches
individuals that their success is the defeat of others. As a result, when placed into higher roles, employees
shutdown, become ineffective, and consequently, they are considered incompetent. Later on, Lazear (2004)
argued that decline in an employee’s ability after promotion is actually the natural outcome of a statistical
process. It displays regression to the mean and therefore Peter Principle is a necessary consequence of any
promotion rule, as the expected ability of those promoted is naturally lower after promotion than before.
c1. To avoid incompetence, training methodologies should be used
Cummings (1971) and Rimler (1971) stated that proper training and employee development programs are the
answer for creating strong and robust organizations. In their opinion, if managers embrace robust learning
initiatives, the Peter Principle can be nullified. Moreover, it was emphasized that the performance review
process has to be designed for the purpose of self-development with provisions for guiding, counseling and
training and all managers have to be taught to motivate, lead and control the activities of their subordinates
(Anderson, Dubinsky and Mehta, 1999). Cann and Cangemi had approached, also in 1971, the idea that, in the
short run, each employee has a unique competence plateau that could be increased through education and
c2. To avoid incompetence, organizational design of conventional hierarchies needs to be reconsidered
Shull and Mosely (1970) argued that conventional structures and bureaucratic controls no longer keep pace
with technological advances required by firms. They asserted that modern employees must participate and be
involved in the management process, and they pleaded for on-going organizational relationships.
Consequently, as the nature of the organizational structure partially determines the style of supervision,
evaluation and promotion, and implicitly the type of leadership, the former needs to be changed in the same
vein. Tracy (1972) concluded that vertical organizational structures are the root of all evil. He also argued that,
in order to survive, a dominant hierarchy must create and maintain a “parahierarchy” composed of members
of a subordinate class to whom the Peter Principle does not apply.
c3. To avoid incompetence, more effective promotion criteria have to be identified
In an article on the promotion of engineers to management, Gately (1996) found that technical ability was
often the number one factor for promotion. Although the study pointed out author’s concern that technical
engineering ability is not a strong indicator of management success, it was asserted that Peter Principle can be
avoided, as long as promotion is based on technical merit and accomplishment. Later on, Buchman (2010) and
Pluchino, Rapisarda and Garofalo (2010) explored alternative promotion tactics and concluded that
randomization is the most effective strategy, despite the possible poor morale and alienated workers resulted.
After all, it appears that not much has truly changed in the many years since Laurence J. Peter formulated his
principle. The literature review performed in this paper is a strong evidence of the fact that the Peter Principle
is still thriving and can still be found in most of the organizations.
4. Envisioned studies on Peter Principle
Considering what has been written until now on the manifestation of Peter Principle in organization, we have
highlighted a number of areas for future research which would, on the one hand, help solving the dilemma
regarding its existence, and, on the other hand, help improve HR promotion strategies.
A. Psychological aspects of Peter Principle
Proceedings of 2100 Projects Association Join Conferences 5 (2016) X-X 5
First of all, the psychological profile of those employees most prone to end up in a situation of incompetence
after being promoted merits further investigation. Several psychological characteristics such as the need for
achievement, Machiavellianism, self-awareness etc. could have an effect on the likelihood of accepting
positions for which the person is not entirely qualified. Moreover, there could be some psychopathic traits
which make certain individuals desire to be constantly promoted and there could be certain fields of activity in
which the desire for career climbing is higher than others. From a different perspective, the psychological
effects that the Peter Principle has on those who realize they are in a position of incompetence also deserves
further attention, especially in regards to the ways in which these affect the possibility to learn and increase
capabilities as argued by Patz (1975). Lastly, the application of Peter Principle to cases of deliberate
incompetence is also interesting. These employees perform their work duties at a level of incompetence that
does not warrant them being fired and require extra pay for doing serious work. In this case, they rarely make
mistakes and they might actually get promoted.
B. Difficulties related to the establishment of criteria used for promotion
Firstly, given the fact that nowadays there is a focus on team work, we need to investigate the means for
effective evaluation of the employee proposed for promotion. These would need to distinguish between whole
group competencies and those exhibited by the individual employee. Secondly, there is a need to analyze the
influence of “favorable circumstances” or “pure luck” and the actual competences and, following Dickinson and
Villeval (2012), shed light on the manifestation of Peter Principle in empirical settings by considering selection
bias and the measurement of “luck”. Thirdly, further research is necessary on how the new employee-employer
compact (the agreement between companies and employees in terms of commitment and responsibilities)
affects the manifestation of the Peter Principle. Hoffman, Casnocha and Yeh (2013) argue that the current
labor market is no longer based on the idea of advancing up the ladder in single company and that employees
nowadays tend to seek promotion opportunities outside their current places of employment. Acosta (2010)
studied the difference in promotion opportunities for incumbent versus external hires, but there is still more
work to be done to establish how these briefer periods of employment affect the probability of a certain
organization to fall in the Peter Principle trap. Lastly, if an employee does not perform well on a lower level
position due to various reasons (poor recruitment, unavailable higher positions) should he still be promoted
and how well does the Peter Principle apply to this type of situation. Is a new corollary necessary?
C. Establishing the conditions for the Peter Principle in an organization
Firstly, it is necessary to establish how long the accommodation period on a new position should be in order to
accurately declare that the employee is incompetent, something which Lazear (2004) discusses in his study.
Secondly, research should enlighten how likely a company is to promote a less competent person instead of a
more competent one and even push the latter to resign. This is in regards to hierarchical exfoliation: super-
competent employees often get stuck in their ranks or get dismissed in order to preserve the hierarchy. The
persons on top of the hierarchy, wishing to remain in power, choose associates that are not competent enough
to remove them from power. Thus, is there any association between the organizational culture or field of
activity and the above-mentioned approached? Thirdly, how can Peter Principle be triggered by paternal in-
step when a family member is promoted several steps above his level of incompetence and what are the
consequences of this situation for organizational morale (e.g., considerable ill feeling towards the new
appointee might arise) and for the individual (e.g., the negative effects of Peter Principle mentioned by Peter
and Hull (1969)). Finally, researchers should also look at the way in which Peter’s inversion manifests in
organizations. This happens when employees have little or no capacity for independent judgment, always obey
and never decide. These are the kind of workers who show obsessive concern with executing job requirements
correctly, permitting no deviations from the established routine. To a person who follows the professional
automaton, paperwork is more important than the purpose for which it was originally designed, in other
words, means are more important than ends. Unfortunately, the automaton appears to be competent from the
hierarchy’s point of view and could be considered for promotion and end up in a position where he no longer is
capable of making decisions. It is at that point that he reaches his level of incompetence. These people are
often managed by incompetent managers who care more about sycophancy and courtesy towards bosses, than
one’s internal efficiency.
6 Proceedings of 2100 Projects Association Joint Conferences 5 (2016) X-X
5. Conclusions
There is nothing about being a great surgeon or educator that actually prepares them to manage a hospital or
an educational institution. In the same vein, the skills necessary for running a successful political campaign
have little to do with those required for governing a county or a country. Unconsciously or unconcerned with
possible consequences, many organizations promote good performers based on their up to that point
achievements, irrespective of their relevancy for the future acquired position. Thus, they often end up with
incompetent decision-makers and lose their super-competent employees. On the other hand, painfully funny is
that most of the employees that validate the Peter Principle do not realize that reaching such a position in the
hierarchy has detrimental effects for both themselves and the organization. It works similar to a paradox: the
more motivated are employees to work hard for proving their competence, the faster is their climb on the
hierarchical ladder, and the sooner most of the higher level managerial positions risks to be filled with too poor
holder of managerial skills.
However, understanding the triggering factors for this paradoxical situation, the favorable conditions for it to
emerge and flourish, as well as its possible consequences would help fighting against it, or, at least, wittingly
make decision. This is what the present article pleads for.
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Business Horizons, 42(1), pp. 19-26.
Baleanu, V. (2007) The economic basis in organizational behavior behavioral theory of the firm, Annals of the University of
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Beeman, D. R. (1981) A public execution of the Peter Principle, Business Horizons, pp. 48-50.
Bernhardt, D. (1995) Strategic Promotion and Compensation, Review of Economic Studies, 62(2), pp. 31539.
Buchman, M. (2010) Incompetence rules. New Scientist, pp. 67-69.
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ResearchGate has not been able to resolve any citations for this publication.
Full-text available
An important issue in personnel economics is the design of efficient job allocation rules. Firms often use promotions both to sort workers across jobs and to provide them with incentives. However, the Peter Principle states that employees' output tends to fall after a promotion. Lazear (2004) suggests that self-selection may improve job allocation efficiency while preserving incentive effects. We reproduce this Peter Principle in the laboratory and compare the efficiency of a promotion standard with subjects self-selecting their task. We find no evidence of effort distortion, as predicted by theory. Furthermore, we find that when the Peter Principle is not severe, promotion rules often dominate self-selection efficiency of task assignment. Results are consistent with imperfect appraisal of transitory ability and a lack of strategic behavior.
Wondering if the Peter Principle is still relevant-individuals in an organization rise to their level of incompetence-we re-examined Dr. Laurence Peter's study of 1969, The Peter Principle-Why Things Always Go Wrong, which achieved best-seller ranking and soon became a part of the lexicon of the business world.We studied, through face-to-face interactions with various employees in eight organizations, whether the concept of incompetence is still in effect. This paper shows that the Peter Principle, the marvel in which employees, around the world, are said to rise to their level of ineffectiveness is still widespread today and that little regarding its use has changed since 1969. Ironically, seventy-three percent of the respondents in my study said that they have seen a Peter Principle condition happen within the last five years, while some of the participants did not agree that the Peter Principle even exists.The behaviors personified in the Peter Principle still have disturbing effects that occur only too regularly in organizations. As a result, the Peter Principle cannot be overlooked. Its effects, nevertheless, can be resolved through extensive training of those who are promoted.We conclude that occupational incompetence is always seen through the eyes of others.
The now famous “Peter Principle” asserts that every manager has a unique executive ability potential and that this ability ceiling or upper limit leads to an inevitable growth in the gap between an organization's demands and the ability of any executive to meet them. In fact, this assertion is shown to be misleading after a formal analysis of two deceptively simple questions. First, how does executive ability develop over time as a manager ascends the leadership ladder; and second, how does this ability compare with an organization's demand for ability at any given time? The result of this analysis is a demonstration that executive ability does increase with the growth in organizational demands, but the increase is cyclical rather than uniform. Additional results are noted concerning the value of executive development programs and the relationship of personal or self problems to organizational problems.
This article proposes that incompetence in management may not be explained so much by the ‘Peter Principle’, i.e. by terminal weaknesses of personnel in faulty promotion systems, as it is by the organizational climate in which managers perform, i.e. by outmoded supervisory styles and limiting structural relationships. This alternative explanation is supported by Townsend's popular book, Up the Organization,¹ where Theory X styles of leadership, in some combination with bureaucratic elements of structure, are seen as impairments in modern organizations.
In this paper, a realistic Markovian model of hierarchies is considered which reveals that under suitable conditions The Peter Principle applies. That is, above a certain critical hierarchical level, performance decreases slowly, but steadily, with increasing level. This can be true even if there is effective screening and promotion is by merit, rather than seniority. Screening procedures which are uniform, realistic and selective can actually decrease relative performance after promotion. Criteria for the manifestation of this phenomenon will be presented. Basically, it is more likely to manifest itself in bureaucracies having low internal mobility and appears when people who are passed over for promotion improve more with another year's experience than those promoted to new jobs which are unfamiliar and more challenging. Mathematically, the controlling parameter is the ratio of two eigenvalues, each the largest eigenvalue of a 3 \times 3 matrix. These eigenvalues are respectively those of two transition matrices, one describing reclassification of successful candidates after promotion, and the other, the reclassification of unsuccessful candidates.
The "Peter Principle" (Peter and Hull, 1969; Fairburn and Malcomson, 2001; Lazear, 2004) suggests that individuals are "promoted to their level of incompetence". A corollary of the "Peter Principle" prediction is that external hires should have an advantage when competing with incumbents for a higher position. Using five years of personnel records from a single large U.S. corporation, this paper contributes to the literature on internal labor markets and intra-firm job mobility by testing this prediction for career advancement. Results support the idea of differences in promotion dynamics among incumbents and external hires, since past career advancement within the firm result in a lower probability of subsequent promotion, even after controlling for workers' heterogeneity and tenure on the current job. The advantage for external hires does not hold once other job changes (lateral transfers, task reorganizations) are considered, highlighting that promotions are a very different job placement mechanism than transfers. Overall, the evidence points out towards declining performance following promotion, as opposed to alternative competing hypothesis of probation placement or "handicapping" external candidates.
In the late sixties the Canadian psychologist Laurence J. Peter advanced an apparently paradoxical principle, named since then after him, which can be summarized as follows: {\it 'Every new member in a hierarchical organization climbs the hierarchy until he/she reaches his/her level of maximum incompetence'}. Despite its apparent unreasonableness, such a principle would realistically act in any organization where the mechanism of promotion rewards the best members and where the mechanism 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 to each other. Here we show, by means of agent based simulations, 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 unavoidable, but also it yields in turn a significant reduction of the global efficiency of the organization. Within a game theory-like approach, we explore different promotion strategies and we find, counterintuitively, that in order to avoid such an effect the best ways for improving the efficiency of a given organization are either to promote each time an agent at random or to promote randomly the best and the worst members in terms of competence. Comment: final version published on Physica A, 10 pages, 4 figures, 1 table (for on-line supplementary material see the link: