Expectation-Driven Generalization of the Peter Principle

The Peter Principle states that individuals in hierarchical systems tend to be promoted until they reach a level of incompetence. Despite its popularity, the principle has remained qualitative. In this paper, we present a mathematical formulation based on expectation-driven success dynamics. We show that incompetence arises when the growth rate of social expectation exceeds the growth rate of capability. The classical Peter Principle emerges as a special case of a universal threshold dynamics applicable to education, early academic success, and public recognition.