  Hierarchy is one of the most conspicuous features of numerous natural,
technological and social systems. The underlying structures are typically
complex and their most relevant organizational principle is the ordering of the
ties among the units they are made of according to a network displaying
hierarchical features. In spite of the abundant presence of hierarchy no
quantitative theoretical interpretation of the origins of a multi-level,
knowledge-based social network exists. Here we introduce an approach which is
capable of reproducing the emergence of a multi-levelled network structure
based on the plausible assumption that the individuals (representing the nodes
of the network) can make the right estimate about the state of their changing
environment to a varying degree. Our model accounts for a fundamental feature
of knowledge-based organizations: the less capable individuals tend to follow
those who are better at solving the problems they all face. We find that
relatively simple rules lead to hierarchical self-organization and the specific
structures we obtain possess the two, perhaps most important features of
complex systems: a simultaneous presence of adaptability and stability. In
addition, the performance (success score) of the emerging networks is
significantly higher than the average expected score of the individuals without
letting them copy the decisions of the others. The results of our calculations
are in agreement with a related experiment and can be useful from the point of
designing the optimal conditions for constructing a given complex social
structure as well as understanding the hierarchical organization of such
biological structures of major importance as the regulatory pathways or the
dynamics of neural networks.
