Mathematical model illustrates our online 'copycat' behaviour | University of Oxford
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Users were influenced by the recent apps downloaded on friends' Facebook pages.
Users were influenced by the recent apps downloaded on friends' Facebook pages.Credit:

Mathematical model illustrates our online 'copycat' behaviour

Researchers have developed a mathematical model to examine online social networks, in particular the trade-off between copying what friends download and relying on ‘best-seller’ lists.

The researchers from the University of Oxford, the University of Limerick, and the Harvard School of Public Health looked at how we are influenced in the choice of apps we download on our Facebook pages by creating a mathematical model to capture the dynamics at play. They found that Facebook users' choice of app was more influenced by friends' behaviour than by seeing Facebook’s equivalent of best-seller lists. The model suggests users tended to be swayed by  activity on their friends' Facebook pages viewed on their Facebook feeds over the previous couple of days. The research, published in the journal, Proceedings of the National Academy of Sciences, finds that there is a strong 'copycat' tendency in human behaviour and we are influenced by the activities of others over a relatively short period of time.

The mathematical model examined data from an empirical study published in 2010, which had tracked 100 million installations of apps adopted by Facebook users during two months. In the 2010 study, based on data collected in 2007, all Facebook users could see a list of the most popular apps (similar to best-seller lists) on their pages, and were also notified about their friends’ recent app installations. In the 2010 study (which included two of the authors of the new study), researchers found that in some cases, users were virtually unaffected by the activities of others, whereas sometimes they were strongly affected  – even though the apps in both these categories did not appear to be distinguished by any particular characteristics. Instead, once an app reached some popularity threshold (as measured by the installation rate), its popularity tended to rise to stellar proportions.

In the new study, the researchers developed a mathematical model to distinguish between the two distinct, competing mechanisms that appeared to drive the dynamics behind the behaviour of the Facebook users. Using their model and extensive computer simulations, they looked behind the empirical data to see whether Facebook users’ behaviour could be modelled as driven primarily by the notifications of apps that had been recently downloaded on their friends’ Facebook pages or  whether it was by the apps listed as best-sellers. Using the supercomputers of the Irish Centre for High-End Computing (ICHEC), the researchers ran thousands of simulations in which they varied the relative dominance of the two influences (recent installations versus cumulative popularity). It took the researchers 15,000 hours of computer processing to match the results of the simulations with the characteristics of app installation observed in the earlier empirical study.

The researchers found that, although users seem to be influenced by both, the stronger effect on popularity dynamics was caused by the recent behaviour of others. The best-seller list did have a ‘mild’ effect on the behaviour of Facebook users, but an instinct to copy others was far more dominant. 

Associate Professor Felix Reed-Tsochas, James Martin Lecturer in Complex Systems at the Said Business School and Director of Complexity Economics at the Institute for New Economic Thinking at the University of Oxford, said: 'We have used sophisticated modelling techniques to show how it is possible to tease apart different causal mechanisms that underpin behaviour even when the empirical data are purely observational. This is significant because the assumption these days is that only experimental research designs can provide such answers. Here, we found that the ''copycat'' tendency plays a very important role in online behaviour. This might be because users need to make quick decisions in information-rich environments, but other research has identified similar imitative behaviour in the off-line world.'

Professor James Gleeson, from the Department of Mathematics and Statistics at the University of Limerick, said: 'This study reveals how we can explore different scenarios using mathematical models to disentangle what drives people to behave the way they do using large data sets from the real online world. This opens up lots of new possibilities for studying human behaviour.'

Commenting on the significance of the method behind the study, Associate Professor Mason Porter, from the Mathematical Institute at University of Oxford, said: 'We hope that our paper can help serve as a guide for modelling complex systems and how data can be incorporated directly into such modelling efforts. The importance of mathematical modelling often seems to be lost amidst the overabundance of empirical studies, and I cannot stress enough that mathematics is also crucial to help illustrate how things work.'

The other authors of the new study were Dr Davide Cellai (University of Limerick) and Assistant Professor Jukka-Pekka Onnela (Harvard). The data used by the research team contained no information about individuals, only information about individual applications.