Abstract
Extensive empirical evidence suggests that there is a maximal number of people with whom an individual can maintain stable social relationships (the Dunbar number). We argue that this arises as a consequence of a natural phase transition in the dynamic self-organization among N individuals within a social system. We present the calculated size dependence of the scaling properties of complex social network models to argue that this collective behavior is an enhanced form of collective intelligence. Direct calculation establishes that the complexity of social networks as measured by their scaling behavior is nonmonotonic, peaking around 150, thereby providing a theoretical basis for the value of the Dunbar number. Thus, we establish a theory-based bridge spanning the gap between sociology and psychology.
Highlights
Extensive empirical evidence suggests that there is a maximal number of people with whom an individual can maintain stable social relationships
On the basis of archeological, evolutionary, and neurophysiological evidence, that 150 is the limit on the number of people with whom a typical person can maintain stable social relationships [1, 2]. We suggest that this is a consequence of internal dynamics producing self-organized criticality within a social network consisting of N people
Assuming that time and complexity are directly proportional [28, 29], the elimination of one is equivalent to the elimination of the other in the allometry relation between the average number of people in a social group and the average cognitive measure in the social brain allometry relation (SBAR). From this we establish by numerical calculations that the Dunbar number is the optimal group size
Summary
Extensive empirical evidence suggests that there is a maximal number of people with whom an individual can maintain stable social relationships (the Dunbar number). The inverse power law index in both network models is shown by direct calculation to increase rapidly in magnitude from 0.5, reach a maximum of ∼0.67, and decrease slowly back to 0.5, as the size of the network increases This nonmonotonic dependence of the scaling index on network size is a signature of complexity [4] and is used to argue that the collective social behavior at criticality supports optimal information transmission within the group. The calculations presented yield a theory-predicted value of the maximum group size that closely agrees with the empirical Dunbar number, as well as showing that networks of this size have optimal information transmission properties These results provide a theory-based bridge that uses network science model calculations to span the current conceptual gap between psychology and sociology. This universal behavior is manifest in the scaling behavior of certain system parameters called critical exponents, on which there is a vast literature
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