Mathematical Theory of Social Conformity I: Belief Dynamics, Propaganda Limits, and Learning Times in Networked Societies
Bibliographic record
Abstract
This paper develops a novel probabilistic theory of belief formation in social networks, departing from classical opinion dynamics models in both interpretation and structure. Rather than treating agent states as abstract scalar opinions, we model them as belief-adoption probabilities with clear decision-theoretic meaning. Our approach replaces iterative update rules with a fixed-point formulation that reflects rapid local convergence within social neighborhoods, followed by slower global diffusion. We derive a matrix logistic equation describing uncorrelated belief propagation and analyze its solutions in terms of mean learning time (MLT), enabling us to distinguish between fast local consensus and structurally delayed global agreement. In contrast to memory-driven models, where convergence is slow and unbounded, uncorrelated influence produces finite, quantifiable belief shifts. Our results yield closed-form theorems on propaganda efficiency, saturation depth in hierarchical trees, and structural limits of ideological manipulation. By combining probabilistic semantics, nonlinear dynamics, and network topology, this framework provides a rigorous and expressive model for understanding belief diffusion, opinion cascades, and the temporal structure of social conformity under modern influence regimes.
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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 | 0.002 | 0.013 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".