Impact of individual actions on the collective response of social systems

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 $\eta=R/A$. 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.