The polarizing effect of network influences

In social networks, opinions and behaviors tend to spread quickly. When an idea seeks to gain attention, success requires both attracting individual users and a careful understanding of cascading behavior -- an idea that attracts a small set of highly influential individuals can easily overwhelm an idea with a much larger, but less influential, support base. Understanding exactly how the choices of individuals propagate through a network, however, poses significant challenges. In this work, we consider a model recently studied by Chierichetti, Kleinberg, and Panconesi (EC 2012) to model cascading behavior when members of a social network must each choose one of two opposing ideas. The model captures the struggle between a desire to follow personal preferences and to match the choices of those you interact with. In this model, observed choices can look much different than the underlying preferences of individuals in the social network, due to cascading of behavior from individuals following their neighbors' lead. In this work, we seek to understand how these quantities can differ. We give strong bounds on adoption rates in terms of underlying preferences, strengthening results of the aforementioned work. Furthermore, our results hold both for richer types of influence between individuals and under weaker assumptions on the underlying preferences of individuals than those previously studied. Notably, we derive bounds that are robust to certain types of correlation between the personal preferences of agents, allowing for our results to be applied to a wider range of settings than prior works which required complete independence between individuals.