Impact of individual actions on the collective response of social systems

• Published in: Scientific reports 2020-07, Vol.10 (1), p.12126-12126, Article 12126
• Main Authors: Martin-Gutierrez, Samuel, Losada, Juan C., Benito, Rosa M.
• Format: Article
• Language: English
• Subjects: 639/705/1041; 639/705/1046; 639/705/531; 639/766/530/2801; Collaboration; Control theory; Efficiency; Humanities and Social Sciences; Mathematical models; multidisciplinary; Probability; Probability distribution; Random variables; Science; Science (multidisciplinary); Social networks; Statistical analysis; Statistical models; Verbal communication
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/s41598-020-69005-y

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.