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The Spontaneous Emergence of Social Influence in Online Systems
J. -P. Onnela, F. Reed-Tsochas
TL;DR
The paper examines whether online adoption data reveal distinct regimes of collective behaviour. Using breakpoint and fluctuation-scaling analyses of application activity, it finds evidence for a structural change separating two regimes with closely similar scaling exponents.
Problem
The analysis addresses whether application activity exhibits a structural change separating distinct behavioural regimes.
Method
The paper combines fluctuation-scaling analysis with breakpoint analysis based on the relative height and narrowness of the F-statistic maximum.
Results
The F-statistic develops a clear maximum, supporting two data regimes with scaling exponents α ≈0.84 and α ≈0.87.
Takeaways & Limitations
Online application activity shows evidence of a structural transition between two regimes rather than a single uniform scaling pattern.
Takeaways & Limitations
Interpreting the temporal fluctuation-scaling exponents requires access to micro-level data.
Abstract
from arXiv · showhide
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.
Methods
The study constructs deterministic, rank-order-preserving synthetic time series to isolate popularity effects from other factors. These series preserve current global rank, making future popularity depend systematically on rank while approximating combined global and local signals.
- Synthetic time-series construction: Synthetic time series are constructed by cutting empirical time series into pieces and recombining them according to global application rank.The construction is deterministic apart from ties and uses a rank-based rule.
- Synthetic time-series construction: For each rank i, the synthetic increment ˜f_i(t) equals the change in installations of the application that held rank i at the previous time step.The synthetic series are initialized with ˜n_i(1) = n_(i)(1) and then recursively updated for t ≥ 2.
- Popularity control: The synthetic series maintain constant relative popularity through global rank, so future popularity is systematically driven only by current popularity.Without rank crossings, the synthetic data would behave like the empirical data.
- Signal decomposition: Synthetic increments combine local and global signals, with the global signal fixed by rank and the local signal representing a mean-field approximation across contributing applications.Each synthetic series typically combines several empirical time series.
Supplementary Information
The supplementary information formalizes temporal fluctuation scaling and interprets its exponent through correlations among application-adoption variables. It also examines stationarity assumptions and supports the existence and robustness of the two-regime crossover.
- Temporal fluctuation scaling: Temporal fluctuation scaling divides additive signals into time blocks and characterizes activity fluctuations through the variance across blocks.The scaling exponent α_T lies in [1/2, 1] and distinguishes temporal averages from ensemble fluctuation scaling.
- Stationarity assumptions: 97.8% of the time series are stationary under the low-density criterion, allowing temporal fluctuation-scaling exponents to be interpreted as correlations.The criterion treats applications with at most 1% of users as sufficiently stationary; stationarity is expected to break down above µ* ≈ 414.
- Stationarity assumptions: The stationarity-based scaling in Fig. 2C remains valid over more than two orders of magnitude above the crossover point µx.The supplementary analysis concludes that the system is sufficiently stationary for the exponents to retain their correlation interpretation.
- Crossover analysis: The empirical error landscape develops a smooth maximum and provides strong evidence for a structural change between the two regimes.Synthetic data instead produce a more rugged, apparently degenerate landscape, with a single maximum at F(k) ≈ 186 for k = 562 and log(µ(562)) ≈ −0.38.