Opinion Dynamics and Influence in Social Networks

Опубликовано 17 августа 2016, 3:13

Almost all important social decisions are taken by individuals on the basis of their opinions, which are formed and updated as a result of their experiences, observations of othersΓÇÖ actions, and news, propaganda and indoctrination from media sources, political leaders and the state. In this talk, we present our recent work on opinion dynamics and influence in social networks. We study a stochastic gossip model of opinion dynamics in a society consisting of two types of agents: regular agents, who update their beliefs according to information that they receive from their social neighbors; and prominent agents with disproportionate impact on the opinions of the rest of the society. We first consider the case when prominent agents obtain some information from others. We show that in this case all beliefs converge to a stochastic consensus. Our main results quantify the extent of their influence by providing bounds or exact results on the gap between the consensus value and the benchmark without prominent agents (where there is efficient information aggregation). We then consider the case when prominent agents are fully stubborn, i.e., they never update their opinions. In this case, opinion dynamics never lead to a consensus (among the regular agents). Instead, beliefs in the society almost surely fail to converge, and the belief of each regular agent converges in law to a non-degenerate random variable. The model in this case thus generates long-run disagreement and continuous opinion fluctuations. We provide explicit characterizations of the expected values and correlations of the limiting beliefs. We also present bounds on the dispersion of the expected values and variances of limiting beliefs as a function of the structure of the underlying social network and the location of the stubborn agents.