Social and Networking Effects on the Online Diffusion of Opinion on a UK Government Petition - A Phase Transition?

Abstract

The UK online Government petition ‘Revoke Article 50’ was both the largest and fastest growing petition ever registered, peak growth achieved 60,000 signatures per hour with the total number reaching 6,087,845. The pattern of signatures followed a sinusoidal curve, consistent with the logistic process and simple epidemic diffusion models such as S:I (susceptible, infected). This suggests that the growth rate of signatures is proportional to the frequency of contacts between actors as opposed to a direct transmission from a single source. I argue that this is also consistent with the “two step flow” (Lazarsfeld & Katz) theory of message diffusion. The assumption behind the logistics process and the S:I model is that of a well mixed homogenous population. Networks like Twitter and Facebook are: homophilic, small-world, long-tailed, exhibit one or more “large components”, and so on. As an alternative I consider threshold models. In particular the work of Watts. The two step flow theory is controversial. Watts,questions whether or not influentials are really influential. He develops simulations to sustain this. These however are centred on random (E_R) networks, and the arguments do not work so well in the context of scale free networks (A_R), where hyper-influentials do exist as the root of the largest trees in s-f distributions. Empirically hyper-influentials did play a role in disseminating Revoke Art 50 retweets. There is psychological evidence of thresholds (personality) in both voting and in following particular websites and that these traits occur in geographical clusters Clusters of vote Remain voters and Revoke Art 50 endorsers are compared. A 1000 vertex scale free network was simulated and diffusion processes with high and low density, central and marginal original tweeters (i.e., either inside or outside a giant connected component, high and low threshold barriers. The objective being to simulate whether Watt’s transition point (“cascade conditions”) would in fact trigger a global cascade as did indeed happen empirically. This did, offer support for Watt’s conjecture but in the context of scale free rather than random networks. A threshold process of this kind could be operating on social networks and that the phase change and subsequent global cascade were the result of the endorsement of “hyper-influentials” who in effect engineered a transition to a high density, low threshold giant hub. I also argue for a qualified revival of the “two step” flow model with hyper-influentials.