Battle of opinions over evolving social networks.

Social networking environments provide major platforms for the discussion and formation of opinions in diverse areas, including, but not limited to, political discourse, market trends, news, and social movements. Often, these opinions are of a competing nature, e.g., radical vs. peaceful ideologies, correct information vs. misinformation, and one technology vs. another. We study the battles of such competing opinions over evolving social networks. The novelty of our model is that it captures the exposure and adoption dynamics of opinions that account for the preferential and random nature of exposure as well as the persuasion power and persistence of different opinions. We provide a complete characterization of the mean opinion dynamics over time as a function of the initial adoption, as well as the particular exposure, adoption, and persistence dynamics. Our analysis, supported by case studies, reveals the key metrics that govern the spread of opinions and establishes the means to engineer the desired impact of an opinion in the presence of other competing opinions.