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An arrogance-competence theory in human organizations is developed by the axiomatic approach to theory development. The evolved theory states that a person’s degree of arrogance heightens as function of increased levels of insecurity as a method for compensating for his perceived inadequacies and that such degree of arrogance bears on job performance and competence ultimately, defining the performance of an organization. Each person defines an ordered pair (arrogance, competence) for himself and interacts with other persons in the organization who also possess the ordered pair characteristics. The interactions of these individuals in an organization describe an interesting dynamical system which relate to chaos theory through a dyadic function or Bernoulli function having an invariance measure equal to a beta probability distribution. Further, the paper explored the relationship between the pair arrogance-competence and individual productivity in relation to the overall organizational productivity. Under the invariant measure, the index of organizational productivity of a large theoretical organization is shown to be about 97%. To maximize organizational productivity, the number of people with high arrogance measures needs to be minimized. This confirms the policies of two large companies: Matsushita Electric Industrial Co., the largest manufacturer of consumer electric appliances in the world, and Norberto Odebrecht, who founded Construtora Norberto Odebrecht, a Latin America conglomerate in engineering, construction, chemicals, mining and oil, in 2007 which provided for disincentives for arrogant behavior in the work place.

Keywords - arrogance scale, competence scale, compensating mechanism, performance, chaos and bifurcation