Peter and Anti-peter Principle as the Discrete Logistic Equation

In this work Peter principle (in the hierarchical structure any competent member tends to rise to his level of incompetence) is consistently interpreted as the discrete form of the well-known logistic (Verhulst or Maltusian) equation of the population dynamics. According to such interpretation anti-Peter principle (in the hierarchical structure any incompetent member tends to rise to his level of competence) is formulated too. As it is well-known remarkable Peter principle [1], [2] states that in the hierarchical structure any competent member tends to rise to his level of incompetence. Even if Peter principle is seemingly paradoxical it is in a satisfactory agreement with situations existing in real social hierarchical structures. There are different attempts of the interpretation or mathematical foundation of Peter principle. In this work an original interpretation will be suggested. Namely, in this work Peter principle will be consistently interpreted as the discrete logistic (Verhulst or Maltusian) equation of the population dynamics. According to such interpretation anti-Peter principle (in the hierarchical structure any incompetent member tends to rise to his level of competence) is formulated too. Thus, as it is well-known logistic (Verhulst or Maltusian) equation in the population dynamics has form dx dt = ax(1− x r ) for a, r > 0 and x ≤ r (1) where t represents the time moment, x (human or some other species) population, a growth parameter and r carrying capacity. Simple solution of this equation, representing a sigmoid function, is x = x0r exp[at] 1 r − x0 − x0 exp[at] (2) where x0 represents the initial population smaller than r. Obviously, when t tends toward infinity x tends toward r and dx dt toward zero. Given logistic dynamics describes population growth limited by negative species self-interaction. It is well known too that there is anti-logistic equation corresponding to (1) dx dt = −ax( x r − 1) for a, r > 0 and x ≥ r (3)