  Social influence drives both offline and online human behaviour. It pervades
cultural markets, and manifests itself in the adoption of scientific and
technical innovations as well as the spread of social practices. Prior
empirical work on the diffusion of innovations in spatial regions or social
networks has largely focused on the spread of one particular technology among a
subset of all potential adopters. It has also been difficult to determine
whether the observed collective behaviour is driven by natural influence
processes, or whether it follows external signals such as media or marketing
campaigns. Here, we choose an online context that allows us to study social
influence processes by tracking the popularity of a complete set of
applications installed by the user population of a social networking site, thus
capturing the behaviour of all individuals who can influence each other in this
context. By extending standard fluctuation scaling methods, we analyse the
collective behaviour induced by 100 million application installations, and show
that two distinct regimes of behaviour emerge in the system. Once applications
cross a particular threshold of popularity, social influence processes induce
highly correlated adoption behaviour among the users, which propels some of the
applications to extraordinary levels of popularity. Below this threshold, the
collective effect of social influence appears to vanish almost entirely in a
manner that has not been observed in the offline world. Our results demonstrate
that even when external signals are absent, social influence can spontaneously
assume an on-off nature in a digital environment. It remains to be seen whether
a similar outcome could be observed in the offline world if equivalent
experimental conditions could be replicated.
