Models of Disagreement and Polarization on Social Networks

Today we find ourselves in a world of fake news, targeted advertising, pronounced manipulation attempts and comprehensive disinformation campaigns, all reinforcing the growing disagreement and polarization of public opinion in open societies. This is disrupting political processes necessary for each body politic to formulate and unite behind its goals, to commit to and pursue its own agendas. Such nefarious methods are not new; however, the present problem is exacerbated by the ubiquitous reach of social media with its echo-chambers, allowing for specifically tailored messages to reach their target audiences quite effectively. Hence, contemporary subversion is a fairly sophisticated endeavor based on structural intricacies of social networks. Attempts at countering it must be based on an equally exact foundation.

This talk will introduce two conventional classes of permanent opinion disagreement models; the French-Harray-deGroot model and Friedkin-Johnsen model, both based on conventional graphs with social actors performing convex combinations of quantified opinions over nonnegative graph edges. This class of models is grounded in group psychology experiments, while bearing similarities to cooperative control engineering protocols used for distributed consensus. The final result is an opinion distribution across a social network as an outcome of a dynamic process, supported by stubborn actors. The talk will also shed light on a more recent compelling class of opinion polarization models, the Altafini model, based on signed graphs with actors interacting through protagonistic and antagonistic ties, modelled by positive and negative graph edge-weights. Altafini model, in contrast, stems directly from well-known cooperative control engineering protocols. Moreover, under the crucial condition of structural balance, this opinion dynamics on signed graphs is equivalent to conventional consensus dynamics on nonnegative graphs. The final result, however, is permanent polarization of a social network as an outcome of a dynamic process, supported by the existence of mutually antagonistic clusters.

Finally, some compelling directions of future research will be discussed, in particular how to prevent the onset of structural conditions allowing for society polarization and how to lead a once polarized society over time to a state of neutral compromise. Results in that direction would provide a social network with a measure of much needed resilience to outside interference by effectively reducing the potential of its polarizing effects.