networks, random networks or scale-free networks, however, the result is sensitive to elasticity coefficients of the environmental influence and the average connectivity of networks. Ultimately, the higher the average connectivity of the network is, the fewer opinions remain at the end. During the simulations for certain average connectivity, sensitive areas are discovered unexpectedly. The system in sensitive areas presents determinate randomness so that the number of opinions when reaching equilibrium remains uncertain. We also find that it might be misleading to predict the number of surviving opinions merely based on the characteristic path length of the network, since a short characteristic path length may possibly accompany with a low average connectivity, which determines the systemic dynamics more directly and essentially. We examine the role of information control, and find that few individuals with the highest influence, namely authorities in this paper, can sway the balance of outcomes. In a social structure of small world networks or random networks, increasing the average connectivity facilitates the diffusion of authorities' opinion. However, in the process of decision-making, people will be subject to disturbances from non-authorities. While a moderate average connectivity may be preferable for the public to form a specific opinion in small world or random networks, the role of authorities in a community with a scale-free structure remains immune to the change of the average connectivity. Provided that the influence of individuals is proportional to the number of their acquaintances in scale-free social networks, the smallest proportion of authorities is required to