Dynamics of the Peter Principle

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 × 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.