Enough but not too many: A bi-threshold model for behavioral diffusion
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.020 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".