Impact of individual actions on the collective response of social systems

TL;DR

A theoretical framework composed of three minimal statistical models that contemplate different levels of dependence between A and R is developed, showing that the efficiency distribution presents a universal structure in three systems of different nature: Twitter, Wikipedia and the scientific citations network.

Abstract

In a social system individual actions have the potential to trigger spontaneous collective reactions. The way and extent to which the activity (number of actions$-A$) of an individual causes or is connected to the response (number of reactions$-R$) of the system is still an open question. We measure the relationship between activity and response with the distribution of efficiency, a metric defined as $η=R/A$. Generalizing previous results, we show that the efficiency distribution presents a universal structure in three systems of different nature: Twitter, Wikipedia and the scientific citations network. To understand this phenomenon, we develop a theoretical framework composed of three minimal statistical models that contemplate different levels of dependence between $A$ and $R$. The models not only are able to reproduce the empirical activity-response data but also can serve as baselines or null models for more elaborated and domain-specific approaches.

Figures (10)

• Figure 1: Example of efficiency distribution where the two distinct behaviors that are manifested to each side of the point $\eta=1$ can be appreciated. The data corresponds to the Twitter conversation around the 2015 Spanish General Elections.
• Figure 2: Diagram that summarizes the main characteristics of the three models: Independent Variables (InV), Identical Actors (IdA) and Distinguishable Actors (DiA).
• Figure 3: Efficiency distributions corresponding to the InV model applied to the scientific citations dataset. The plots show the empirical efficiency distribution (blue dots), the Monte-Carlo simulation (orange squares) and the analytical expression of \ref{['eq:inp_eff_distr_res']} (green line).
• Figure 4: Same as figure \ref{['fig:sci_inp_eff']} for the InV model applied to the Twitter datasets.
• Figure 5: Same as figure \ref{['fig:sci_inp_eff']} for the InV model applied to the Wikipedia dataset.