Discussing big news stories online is a common experience among those who use social media. But at what point do people decide to share – or not share – posts with friends, family and followers?

It turns out math could reveal the answer.

Brock University Assistant Professor of Mathematics and Statistics Pouria Ramazi and his international research collaborators from Canada, Iran and Hong Kong have used a mathematical model to predict when individuals will both start and stop behaviours when other people are doing the same thing.

For decades, the “linear threshold model” has provided a framework for understanding the timing of people’s actions. This model assumes each person has a unique tipping point — called the threshold — that determines when they will adopt a behaviour based on the fraction of the population exhibiting it around them, says Ramazi.

“If, let’s say, only 10 per cent of my friends are talking about something, I may not share it,” he says. “But if 50 per cent spread that news, it looks like it is getting important, so I may want to also talk about it.”

What was missing in the model until now was an “upper threshold” to set a cap on when the individual would stop adopting the behaviour, such as talking about the news, says Ramazi.

A bi-threshold model could guide marketers, officials, businesses and others to estimate an approximate level of outreach before overselling their message, he says.

In their recent study, “Enough but not too many: A bi-threshold model for behavioral diffusion,” the researchers say previous social science research has revealed the possibility of this upper threshold through three mechanisms.

One is the “congestion effect,” where someone may want to hit the beach with a few friends, for example, but probably not if the beach is packed.

The second is the “snob effect” in which a fashion-conscious person, for example, will purchase an outfit to stand out from the crowd but will stop wearing it when the clothing becomes too trendy.

The third mechanism, “saturation,” occurs when spreading news, gossip, jokes or other information becomes less appealing as more people know about it.

To test the existence of this upper threshold, Ramazi and colleagues used social media datasets gathered from three situations: the 2012 discovery in physics of a new heavy particle on Twitter, now known as X, coverage of the popular Melbourne Cup horse race on X and discussion on the COVID-19 vaccination campaign on the Chinese social media platform Weibo.

The datasets included measures of social media behaviour — such as postings, likes and mentions — as well as the number of contacts for each user included in the study.

The team used data-driven techniques to group users based on their available information and estimated the lower and upper thresholds for each group based on their social media behaviour.

The researchers then created and evaluated two models for the three situations: one model with just the lower threshold, or point at which people would start sharing information on social media, and another with both a lower and an upper threshold, or point when people would stop sharing.

“The model that used both the lower threshold and the upper threshold was able to better predict the spread of the news in the population, sometimes by orders of magnitude more accurately,” he says. “This suggests that this second, upper threshold does exist in at least some social contexts.”

Ramazi says the findings provide insights into how groups behave, such as how information spreads or new ideas are adopted, and that this knowledge can help improve strategies in areas such as marketing, public health and policy-making. He adds that future research can verify this model in other real-world scenarios and analyze the resulting decision-making dynamics theoretically.