Evolution of Opinions on Social Networks in the Presence of Competing Committed Groups
Published:
Summary
We measured the impact that a small minority of committed individuals in a densely populated social network would have on the group’s overall opinion. We performed our analysis on two types of stylized social network and found that there are regions of phase space where multiple opinions are stable and regions where a minority opinion will dominate.
Contribution
I performed simulations on both weighted and unweighted partially connected graphs using the two-opinion naming game. The two-opinion naming game is a model wherein each node has an opinion either A or B and then shares its opinion with its adjacent nodes. As an example, if a node has an opinion A and has opinion B shared with it, its opinion is now AB. If it has B shared with it again, it has now flipped to opinion B. In our model, we initialized our network to all have an opinion A, we then fixed some fraction of nodes to have opinion B and observed the dynamics of the system.
Abstract
Public opinion is often affected by the presence of committed groups of individuals dedicated to competing points of view. Using a model of pairwise social influence, we study how the presence of such groups within social networks affects the outcome and the speed of evolution of the overall opinion on the network. Earlier work indicated that a single committed group within a dense social network can cause the entire network to quickly adopt the group’s opinion (in times scaling logarithmically with the network size), so long as the committed group constitutes more than about 10% of the population (with the findings being qualitatively similar for sparse networks as well). Here we study the more general case of opinion evolution when two groups committed to distinct, competing opinions A and B, and constituting fractions $p_A$ and $p_B$ of the total population respectively, are present in the network. We show for stylized social networks (including Erdös-Rényi random graphs and Barabási-Albert scale-free networks) that the phase diagram of this system in parameter space $(p_A, p_B)$ consists of two regions, one where two stable steady-states coexist, and the remaining where only a single stable steady-state exists. These two regions are separated by two fold-bifurcation (spinodal) lines which meet tangentially and terminate at a cusp (critical point). We provide further insights to the phase diagram and to the nature of the underlying phase transitions by investigating the model on infinite (mean-field limit), finite complete graphs and finite sparse networks. For the latter case, we also derive the scaling exponent associated with the exponential growth of switching times as a function of the distance from the critical point.
Recommended citation:
Xie, J., Emenheiser, J., Kirby, M., et al. “Evolution of opinions on social networks in the presence of competing committed groups”, 2012 (PLoS ONE 2012)