Consensus Using a Network of Finite Memory Pólya Urns
Bibliographic record
Abstract
We introduce a finite memory interacting Pólya urn process over a connected network which models consensus dynamics for interacting individuals. More specifically, each urn (individual) in the network is initially equipped with some red and black balls, with the fraction corresponding to the individual’s opinion (or belief) on a certain color. At each time instant and for each urn, a ball is drawn from a “super-urn", which consists of all balls present in that urn and its neighboring urns; then reinforcing balls of the color just drawn are added to the urn for a limited period of M future time instants, where M denotes the memory parameter. Additionally, and important for our objective, as of time t=M+1, we remove the balls which were present in the urns initially. By examining the structure of the resulting underlying reducible Markov process, we show that individuals eventually reach consensus in the sense that they all achieve identical probabilities of drawing a red ball. Moreover, when the network has homogeneous reinforcement parameters, we construct a class of linear dynamical systems with time delay whose trajectory gives the probability of drawing a red ball for each node i at a time instant t. We examine the asymptotic behavior of such a network and exactly determine its consensus value. Our simulation confirms our theoretical findings by demonstrating the asymptotic behavior of draw variables of the network in some case studies.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 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 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".