Measuring and moderating opinion polarization in social networks

The polarization of society over controversial social issues has been the subject of study in social sciences for decades (Isenberg in J Personal Soc Psychol 50(6):1141–1151, 1986 , Sunstein in J Polit Philos 10(2):175–195, 2002 ). The widespread usage of online social networks and social media, and the tendency of people to connect and interact with like-minded individuals has only intensified the phenomenon of polarization (Bakshy et al. in Science 348(6239):1130–1132, 2015 ). In this paper, we consider the problem of measuring and reducing polarization of opinions in a social network. Using a standard opinion formation model (Friedkin and Johnsen in J Math Soc 15(3–4):193–206, 1990 ), we define the polarization index , which, given a network and the opinions of the individuals in the network, it quantifies the polarization observed in the network. Our measure captures the tendency of opinions to concentrate in network communities, creating echo-chambers. Given this numeric measure of polarization, we then consider the problem of reducing polarization in the network by convincing individuals (e.g., through education, exposure to diverse viewpoints, or incentives) to adopt a more neutral stand towards controversial issues. We formally define the ModerateInternal and ModerateExpressed problems, and we prove that both our problems are NP-hard. By exploiting the linear-algebraic characteristics of the opinion formation model we design polynomial-time algorithms for both problems. Our experiments with real-world datasets demonstrate the validity of our metric, and the efficiency and the effectiveness of our algorithms in practice.