Stability of certainty and opinion in influence networks
Bibliographic record
Abstract
This paper introduces two models for influence in networks, and presents some upper and lower bounds for time needed to reach stability in these models. The first, called the Majority Model, is an expansion on the “Democrats and Republicans Model” that uses cascades to initialize the influence network rather than randomly assigning each node an initial opinion. By slightly modifying a network introduced by Frischknect, Keller, and Wattenhofer [10] to fit the specifications of the Majority Model, we show that Frischknecht et al.'s lower bound for stability of Ω(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3/2</sup> ) on the Democrats and Republicans Model also holds in the Majority Model. The second model, called the Certainty Model, is the same as the Majority Model but with the addition of a variable for a node's certainty in its own opinion. Each node weights the opinions of its neighbors by their respective certainties and moves to the mass center of all of these opinions. For the Certainty Model we obtain two upper bounds related to time to stability. The first is a bound of O(d) for the time to reach stability once all nodes have gained an opinion, where d is the diameter of the graph. The second is a bound of O(n) on the time required for all nodes to gain an opinion.
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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) | 0.000 | 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".