Stabilizing Consensus with the Power of Two Choices
Bibliographic record
Abstract
Consensus problems occur in many contexts and have therefore been intensively studied in the past. In the standard consensus problem there are n processes with possibly different input values and the goal is to eventually reach a point at which all processes commit to exactly one of these values. We are studying a slight variant of the consensus problem called the stabilizing consensus problem. In this problem, we do not require that each process commits to a final value at some point, but that eventually they arrive at a common value without necessarily being aware of that. This should work irrespective of the states in which the processes are starting. Coming up with a self-stabilizing rule is easy without adversarial involvement, but we allow some T-bounded adversary to manipulate any T processes at any time. In this situation, a perfect consensus is impossible to reach, so we only require that there is a time point t and value v so that at any point after t, all but up to O(T) processes agree on v, which we call an almost stable consensus. As we will demonstrate, there is a surprisingly simple rule for the standard message passing model that just needs O(log n loglog n) time for any sqrt{n}-bounded adversary and just O(log n) time without adversarial involvement, with high probability, to reach an (almost) stable consensus from any initial state. A stable consensus is reached, with high probability, in the absence of adversarial involvement.
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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 | 0.007 | 0.029 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.006 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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".