Enough but not too many: A bi-threshold model for behavioral diffusion

Behavioral diffusion is commonly modeled with the linear threshold model, which assumes that individuals adopt a behavior when enough of their social contacts do so. We observe, however, that in many common empirical settings individuals also appear to abandon a behavior when too many of their close contacts exhibit it. The bi-threshold model captures this tendency by adding an upper threshold, which, when exceeded, triggers behavioral disadoption. Here we report an empirical test of the bi-threshold model. We overcome the significant challenge of estimating individuals' heterogeneous thresholds by extending a recently introduced decision-tree based algorithm to the bi-threshold setting. Using the context of the spread of news about three different topics on social media (the Higgs boson, the Melbourne Cup horse race, and the COVID-19 vaccination campaign in China), we show that the bi-threshold model predicts user engagement with the news orders of magnitude more accurately than the linear threshold model. We show that the performance gains are due especially to the bi-threshold model's comparative advantage in predicting behavioral decline, an important but previously overlooked stage of the behavioral diffusion cycle. Overall, the results confirm the existence of the second upper threshold in some contexts of diffusion of information and suggest that a similar mechanism may operate in other decision-making contexts.