Impact of individual actions on the collective response of social systems

TL;DR

This paper investigates how individual actions influence collective responses in social systems, revealing a universal efficiency distribution across platforms like Twitter, Wikipedia, and citation networks, supported by theoretical models.

Contribution

It introduces a universal efficiency distribution in social systems and develops minimal models to explain the activity-response relationship.

Findings

Efficiency distribution is universal across different social platforms.

Theoretical models replicate empirical activity-response data.

Models serve as baselines for further domain-specific studies.

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.