Committed activists and the reshaping of status-quo social consensus

The role of committed minorities in shaping public opinion has been recently addressed with the help of multiagent models. However, previous studies focused on homogeneous populations where zealots stand out only for their stubbornness. Here we consider the more general case in which individuals are characterized by different propensities to communicate. In particular, we correlate commitment with a higher tendency to push an opinion, acknowledging the fact that individuals with unwavering dedication to a cause are also more active in their attempts to promote their message. We show that these activists are not only more efficient in spreading their message but that their efforts require an order of magnitude fewer individuals than a randomly selected committed minority to bring the population over to a new consensus. Finally, we address the role of communities, showing that partisan divisions in the society can make it harder for committed individuals to flip the status-quo social consensus.

Figure 1

Numerical results for convergence time $T_{\mathrm{conv}}$ in the binary NG with a randomly selected committed minority for a population of $N={10}^4$ agents. Only two opinions are possible, $A$ or $B$, with a state of consensus reached when everyone knows only opinion $A$. Committed agents begin with knowledge of $A$ and introduce this new opinion to the rest of the population who initially know opinion $B$. The median of 100 simulations shows that convergence time diverges at the analytically derived critical threshold of $p_c\approx 0.0718$. The $95\%$ and $50\%$ confidence intervals are shown shaded in dark and light gray.

Figure 2

Average number of interactions required to reach convergence $I_{\mathrm{conv}}$ vs $p$ in the NG in activity-driven networks for a population of $N={10}^4$ agents for 100 simulations (top). $I_{\mathrm{conv}}$ diverges at the same $p_c$ for random committed minorities as in systems with homogenous activity distributions (Fig. 1). (Bottom) $\mathit{Activists}$ (commitment correlated with high probability to speak), on the other hand, show considerable advantage in needing fewer interactions to reach consensus and a numerical threshold of $p_c\approx 2\times {10}^{-3}$, agreeing well with the analytically derived $p_c\approx 1\times {10}^{-3}$.

Figure 3

Comparison of average number of interactions required to reach convergence $I_{\mathrm{conv}}$ vs $p$ in the NG in activity-driven networks with $N={10}^4$ agents for $m=1$ and 10 listeners per speaker per time step. $I_{\mathrm{conv}}$ and the critical threshold $p_c$ remain the same despite a tenfold increase in communication per step. Error bars are not visible at the scale of the plot.

Figure 4

$I_{\mathrm{conv}}$ in the NG on a real network of $N=1222$ agents containing two weakly connected communities vs a random rewiring of the network (inset). Agents begin with knowledge of opinion $A$ or $B$ dependent upon the community they are originally a part of with a select group in community $A$ remaining committed to $A$. $I_{\mathrm{conv}}$ is the number of interactions at which $95\%$ or more of the network agrees upon opinion $A$. In both the original community based network and the rewired network, shown in the insets, activists (bottom) show considerable advantage over randomly selected committed minorities (top) in needing fewer committed agents.

Figure 5

$I_{\mathrm{conv}}$ in the NG on a real network of $N=1222$ agents containing two weakly connected communities vs a random rewiring of the network (inset). All agents begin with knowledge of opinion $B$, regardless of their original community membership except for a select group in community $A$ who remain committed to $A$. $I_{\mathrm{conv}}$ is the number of interactions at which $95\%$ or more of the network agrees upon opinion $A$. In both the original community based network and the rewired network, shown in the insets, activists (bottom) show considerable advantage over randomly selected committed minorities (top) in needing fewer committed agents.