Social Networks, in The Critical Mass in Collective Action. Marwell and Oliver (1993)

Variables

Density

In a group of size N, the maximum number of ties is N(N-1)

• Then density is defined as D = T/N(N-1), where T is the number of ties
• For one individual, we have d_i = t_i/(N-1)

Centralisation

Defined as the the standard deviation of the individual densities

• Note that is inverse, in the sense that high SD yields high centralization

Organising Cost

Assume constant cost per agent recruited

Discussion

• Centralisation is a form of heterogeneity
  • It is important because the modal personal network size is typically insufficient to support collective action
• However the positive effect of centralization is counteracted by interest in group organization heterogeneity
  • If the two are independent, then it becomes more likely that the individual with the most ties will not be interested enough
• Selectivity refers to the fact that there is a cost of mobilizing an individual whom you know and, as such, you might only be able to mobilize so many people
  • It implies that larger networks (via centralization) encourage collective action by making it more likely that there are large contributors in the group (rather than having access to more contributors)
• Information helps by allowing selectivity
  • Value of information increasing in heterogeneity of group