Modelling the Influence of Social Media on Collective Opinion

Abstract

When we divide our present society into real and cyber worlds, there exist no clear data on how the public attitude or opinion is formed and on what sort of opinion distribution is realized in the cyber world. We propose a methodology for the model calculation with which we can compare the observation of the public opinion formed under the environment of social media in the cyber world. The public viewpoint or the opinion about a certain matter, together with the standpoint of the information provided by the social media, can not be given by some discrete values, but they make fuzzy distributions within certain ranges of opinion around certain central values. With the assumption that the variation of the public opinion originates from the emotional contagion induced by the contact of the public with the social media, and that the force realized by this contagion is given in terms of the common area of such fuzzy distributions of the public opinion and the information on the social media, we derived an equation of motion for the variation of public opinion. By further assuming that the information diffuses from a top toward a bottom of a ramified tree structure of node networks, we exemplified some characteristic patterns of the distribution of collective opinion including the effect of echo-chamber, which are realized under certain input spectra of the information on the social media. Moreover, by using the observed data for the 2016 USA President election as an input, we made clear that the reversal of the approval rating might possibly occur between the political right and left wings in so far as the response character of supporters to the social media differ depending on the political situation of the public.