A Mathematical Model of Organisational Leadership

Abstract

This paper develops a simple mathematical model to explain the governing dynamics of leadership and followership in an organisation. The model is based on the contingency theory of leadership. It recognizes leadership and followership at various levels of the hierarchy and demonstrates how both leadership and followership style, at each horizontal, is contingent on not just the attributes of the horizontals immediately below and above it, but also to the attributes of every other horizontal in the hierarchy. The paper also demonstrates that a leader can vary certain key variables and cause a predictable change in the weighted contribution of the attributes of a horizontal to leadership styles and followership styles of all workers in an organisation. This technique can be effectively used by leadership programs to identify key variables and achieve a predictable change in work style by influencing those key variables in a customised manner.