The dynamics of group affiliation

Today we present in this blog the work by Nicholas Geard and Seth Bullock about the dynamics of group affiliation-see http://eprints.ecs.soton.ac.uk/21195/5/S0219525910002712.pdf-. Models about group formation are common in many social simulations. But models on group affiliation in which individuals can belong to multiple groups simultaneously are very infrequent. According to Geard and Bullock (art. cit., 2010, p. 501), some types of groups may be exclusive, that is, membership in one group precludes membership in other groups of that type and others are non-exclusive. Affiliation with a group involves the consum of time and energy being very important to determine the degree of commitment of the subjects and their degree of participation in other groups for studying the social evolution.

In pre-modern societies the affiliations were made in a series of concentric social circles from family to the country but in contemporary society all is more complex. In the "liquid society" (so called by Zygmunt), the bonds in choices of affiliation are very complex and fuzzy. Individual may belong to multiple groups simultaneously and Geard and Bullock design a model of affiliation to non-exclusive groups. Their simulation considers a network of n nodes and m undirected edges (art. cit., p. 507), representing individuals and the social ties between them. Each node i has a trait vector of dimension d, representing that individual´s location in social space, a list of affiliated groups and a time and energy capacity. Trait values are bounded between zero and one and are uniformly distributed. The social distance between two individuals is defined as the Euclidean distance between their trait vectors. Each group has a cost of time and energy associated with being a member, reducing the number of groups with which a node can be affiliated.

In the network, edges may be rewired either to nodes sharing a common state, or at random. Nodes may either initiate a new group, or be recruited to an existing group by one of their network neighbors. A node initiating a new group will always leave existing groups to maketime for the new group while a node being recruited to a new group will either leave existing groups or refuse the recruitment attempt, depending of the sociodemographic space.

For the simulations, the authors explored the circumstance where all memberships are exclusive, the population evolving to a "connected community structure" (art. cit., p. 509), that is, a type of continuing connectivity combined with the occasional initiation of novel groups. All groups had a cost of one but increasing cost above one had relevant effects on network structure, decreasing the level of community comparable to that of a random network. this trend suggests that as individuals belong to more groups, they are lees likely to become disconnected from the population, but have more opportunities to leave groups containing different to themselves. Obviously, less costly groups were maintained in the population in greater quantities than more costly groups but the mean size of the more costly groups remained constant as capacity of time and energy increased, while that of the less costly groups grown rapidly.

One interesting prediction is that less costly groups may find it easier to thrive, but that more costly groups may retain more diversity. We believe that the ideas surrounding the simulation by Geard and Bulloch is an interesting step forward for the modelization of the complex problem of the affiliation in social dynamics.