Majority Rule Based Opinion Dynamics with Biased and Stubborn Agents
Bibliographic record
Abstract
In this paper, we investigate the impact of majority-rule based random interactions among agents in a large social network on the diffusion of opinions in the network. Opinion of each agent is assumed to be a binary variable taking values in the set {0, 1}. Interactions among agents are modeled using the majority rule, where each agent updates its opinion at random instants by adopting the 'majority' opinion among a group of randomly sampled agents. We investigate two scenarios that respectively incorporate `bias' of the agents towards a specific opinion and stubbornness of some of the agents in the majority rule dynamics. For the first scenario, where all the agents are assumed to be 'biased' towards one of the opinions, it is shown that the agents reach a consensus on the preferred opinion (with high probability) only if the initial fraction of agents having the preferred opinion is above a certain threshold. Furthermore, the mean time taken to reach the consensus is shown to be logarithmic in the network size. In the second scenario, where the presence of 'stubborn' agents, who never update their opinions, is assumed, we characterize the equilibrium distribution of opinions of the non-stubborn agents using mean field techniques. The mean field limit is shown to have multiple stable equilibrium points which leads to a phenomenon known as metastability.
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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".