The University of Liege in Belgium has done some research modelling how opinions evolve in social networks and how distinct communities can influence each other based on the number of nodes connecting the communities.
The researchers looked at two groups, initially isolated, whose members gradually begin to talk to members of the other group.
They supposed for simplicity that individuals hold one of two opinions, assigned randomly at the start. People then change their views by a “majority rule” – each person tends to adopt the opinion that is held by a majority of those with whom they are linked in the social network.
Solving their model mathematically, the authors found that when the two groups were isolated or nearly isolated, people within each group quickly came to share one opinion but the groups were as likely to agree as disagree with each other.
As Lambiotte and colleagues began adding social links between the groups. But they found no change, at first. The two groups continued to form opinions independently.
But rather than a gradual increase in the way opinions “leak” from one group to the other as more connections are added, the researchers found a surprise when the number of links between the groups reached a precise threshold. Suddenly, the final opinions of the two groups were always identical. Even a few extra links between groups were enough to “tip” their final opinions from a state of full polarization to full agreement.
Journal reference: Physical Review E (DOI: 10.1103/PhysRevE.75.030101)
What's fascinating is the application of this work.. the team suggests for example that the reason why there is persistent polarization among democratic and republican bloggers in the US, is that most bloggers may be reading blogs that predominantly agree with their sentiments to begin with , therefore reinforcing polarizing positions.
This suggests to me that the work may be useful in determining what and how much of a linkage to a prospect community and how many influencers are needed to create a change in perception in that community. I need to learn more about this.