Opinion dynamics on interacting networks: media competition and social influence

Abstract

The inner dynamics of the multiple actors of the informations systems - i.e, T.V., newspapers, blogs, social network platforms, - play a fundamental role on the evolution of the public opinion. Coherently with the recent history of the information system (from few main stream media to the massive diffusion of socio-technical system), in this work we investigate how main stream media signed interaction might shape the opinion space. In particular we focus on how different size (in the number of media) and interaction patterns of the information system may affect collective debates and thus the opinions' distribution. We introduce a sophisticated computational model of opinion dynamics which accounts for the coexistence of media and gossip as separated mechanisms and for their feedback loops. The model accounts also for the effect of the media communication patterns by considering both the simple case where each medium mimics the behavior of the most successful one (to maximize the audience) and the case where there is polarization and thus competition among media memes. We show that plurality and competition within information sources lead to stable configurations where several and distant cultures coexist.

Figure 1. A graphical sketch of our model.

(Left panel) Gossipers interact among themselves choosing a neighbor in their social network (double arrow). If the gossipers have similar ideas, their opinion will converge further (eq.1). (Central panel) Gossipers are also influenced by the media: when they are exposed to information, their opinion will converge to such information if it is not too far from the gossiper's initial opinion (eq.2). (Right panel) Media are subject to a leader-follower dynamics. Media are supposed to have a network of other media with which interact either trying to copy their memes (black lines) or trying to oppose their memes (red dashed lines). Each media chooses to mimic/oppose the most successful (the one with more followers) of its neighboring media (eq.3). These drawings have been realized by AS using the open source clip-part collection at http://openclipart.org/.

Figure 2. Maximal opinion distance d (the difference between the highest and lowest opinion in the gossipers' network) versus tolerance σ.

The size of the symbols is bigger than the error bars. Opinions' distance under the effect of audience-oriented unpolarized media shows a smoothening of the transition (less sharp change of d versus σ).

Figure 3. Localization L versus tolerance σ.

Error bars are of the order of the symbol size. The localization parameter can be thought as the inverse of the number of different opinion; therefore L = 1 for consensus, while a low value of L signals fragmentation of the opinions. (Left panel) Localization in gossip scale-free networks increases with the tolerance when the media are audience oriented agencies (i.e. unpolarized). Notice that full consensus (L = 1) is reached at a tolerance ~ 0.5 like the single-network BCM model case. (Right panel) Localization has a non-monotonic trend when media are polarized; in particular, it reaches a maximum before the tolerance is maximal (σ = 1). Like in the BCM model, opinions are fragmented at low values of σ since they do not interact; unlike the BCM model, consensus is not reached at high values of σ and opinions are fragmented due to the polarization of the media.

Figure 4. Localization L versus tolerance σ for Barabasi-Albert scale-free (BA) and Watts-Strogatz small world (WS) networks with rewiring probabilities p = 0.1, 0.2, 0.3.

Error bars are of the order of the symbol size. The complex networks of gossipers and media are of comparable sizes. (Left panel) For un-polarized media, increasing the tolerance leads toward consensus (L = 1). (Right panel) Polarization among the media produces a reentrant effect on the localization: while at low values of σ opinions are fragmented since they do not interact, at high values of the tolerance polarization induces fragmentation.