(ANTI)PETER Principle - Discrete (INVERSE) Logistic Equation with Imprecisely Estimated and Stimulated Carrying Capacity

TL;DR

This paper models the Peter and anti-Peter principles using discrete logistic equations with imprecise carrying capacity estimates, revealing how control errors influence social, biological, and economic systems and can lead to various phase transitions.

Contribution

It introduces a novel discrete logistic framework for the Peter principles, incorporating estimation errors and control mechanisms to explain complex systemic behaviors.

Findings

Control errors can eliminate paradoxical effects of Peter principles.

Estimation errors lead to social and biological pathologies.

Stimulated boundary levels cause phase transitions in systems.

Abstract

In this work we consider the Peter principle and anti-Peter principle as the discrete logistic and discrete inverse logistic equation. Especially we discuss imprecisely estimated (by hierarchical control mechanism) carrying capacity, i.e. boundary (in)competence level of a hierarchy member. It implies that Peter principle holds two sub-principles. In the first one objective boundary competence level is increased for estimation error. In the second one objective boundary competence level is decreased for estimation error. Similarly, anti-Peter principle holds two sub-principles too. All this implies that paradoxical situations that follow from Peter and anti-Peter principle can be simply removed by decrease of the error of hierarchical (social) control. Also we discuss cases by Peter principle when error of the boundary competence level by estimation grows up. (Then, in fact, there is no estimation error but stimulation of the boundary level by control mechanism.) By first Peter sub-principle it implies anarchy in the social structure or, correspondingly, cancer in the biology and medicine, schizophrenia in the psychology and inflation in the economy. By second Peter sub-principle it implies a totalitary social structure (dictature or caste regime) or multiplex sclerosis and other autoimmune diseases in biology and medicine, servile mentality or low value complex in psychology and depression by hyperactive political influences in economy. Finally, monotonus changes of the stimulated part of boundary level cause corresponding phase transitions discussed on the example of the introspection in the psychology.