Effects of mixing in threshold models of social behavior
Bibliographic record
Abstract
We consider the dynamics of an extension of the influential Granovetter model of social behavior, where individuals are affected by their personal preferences and observation of the neighbors' behavior. Individuals are arranged in a network (usually the square lattice), and each has a state and a fixed threshold for behavior changes. We simulate the system asynchronously by picking a random individual and we either update its state or exchange it with another randomly chosen individual (mixing). We describe the dynamics analytically in the fast-mixing limit by using the mean-field approximation and investigate it mainly numerically in the case of finite mixing. We show that the dynamics converge to a manifold in state space, which determines the possible equilibria, and show how to estimate the projection of this manifold by using simulated trajectories, emitted from different initial points. We show that the effects of considering the network can be decomposed into finite-neighborhood effects, and finite-mixing-rate effects, which have qualitatively similar effects. Both of these effects increase the tendency of the system to move from a less-desired equilibrium to the "ground state." Our findings can be used to probe shifts in behavioral norms and have implications for the role of information flow in determining when social norms that have become unpopular in particular communities (such as foot binding or female genital cutting) persist or vanish.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".