Why weigh at all

Counting is right when every voter is worth the same. A maintainer who has read the code for years, a reviewer who was wrong twice, and a first-time contributor each cast one ballot. A plurality reports them as three equal opinions. DeGroot’s model (doi:10.1080/01621459.1974.10480137) is the standard answer and is one line: each voter replaces its opinion with the weighted average of the voters it trusts, x(t+1) = W x(t). Where that settles is the group’s position, and it is the mean only when trust is symmetric.

When it settles

The iteration converges to agreement exactly when the trust graph has one closed group every voter reaches, and that group is aperiodic (Berger, doi:10.1080/01621459.1981.10477662). Two teams that cite only each other never converge, and that is a fact about the team worth reporting rather than a number worth averaging. The tracker’s own consensus verb reports the split; this crate reports settled: false when the budget runs out.

Anchoring

Friedkin and Johnsen (doi:10.1080/0022250X.1990.9990069) keep each voter partly anchored to its own starting opinion. The step is a contraction for any anchor, so it always settles, and what settles is a profile of persistent disagreement rather than one shared position. That is the setting to use when reviewers are not expected to abandon their reading.

Bounded confidence

Hegselmann and Krause, and Deffuant and colleagues (doi:10.1142/S0219525900000078), let each voter listen only to voters whose opinion lies within a bound of its own. Two blocs further apart than the bound never meet: the model produces clusters where the trust graph alone would produce one position. --epsilon runs that step, and --epsilon-of gives each voter its own bound, which is the shape a persona with a narrow audience takes. Castellano, Fortunato and Loreto review the family (doi:10.1103/RevModPhys.81.591).

Reading a settle

Two numbers come with every outcome. Polarization is how far the final opinions sit from their mean, summed over voters; disagreement is how far neighbours sit from each other, weighted by the trust between them, summed over edges. Musco, Musco and Tsourakakis (doi:10.1145/3178876.3186103) show the two move against each other under the Friedkin-Johnsen step, so a network can be tuned to lower their sum. A settle that reports high polarization and low disagreement has agreed within blocs that do not hear each other; the shares alone would not show it.

Panels of agents

Running several model calls and settling their answers is now a product feature. Self-consistency samples one model many times and takes the majority (Wang et al., doi:10.48550/arXiv.2203.11171). Multi-agent debate lets several instances read each other’s answers over rounds before a final vote (Du et al., doi:10.48550/arXiv.2305.14325; Liang et al., doi:10.48550/arXiv.2305.19118), and a jury of debating evaluators grades text the same way (ChatEval, doi:10.48550/arXiv.2308.07201). Mixture of agents feeds the answers of several models to an aggregator model that writes the final one (Wang et al., doi:10.48550/arXiv.2406.04692). One model can also play several personas and have them collaborate (Wang et al., doi:10.48550/arXiv.2307.05300), and the roster can be chosen per task (Liu et al., doi:10.48550/arXiv.2310.02170). Debate between more persuasive models makes a weaker judge more truthful (Khan et al., doi:10.48550/arXiv.2402.06782). A commercial system runs several agents in parallel on “multiple hypotheses at once” and settles before answering (the Grok 4 announcement, https://x.ai/news/grok-4); reports describe a captain agent deciding when the others do not agree, which this crate has not verified against a primary source.

Two things these share, and this crate does differently. First, the aggregation is a count or an aggregator model’s judgement, with every voice weighed the same; Chen et al. (doi:10.48550/arXiv.2403.02419) show that adding calls to such a count is not even monotone in accuracy, since it helps on easy items and hurts on hard ones. Here the aggregation is a weighted settle whose weights are memory: rows a person set, rows learn moved when an outcome refuted a voter, rows calibrate wrote from the voters’ history, each scoped to the topics they were earned on. Second, the roles are prompts that vanish with the session; here a persona is an atom in the pack with an anchor the settle honours, and a captain who decides when the panel splits is one persona with an anchor of zero, not a special case. The settle also says how the panel split, in polarization and disagreement, where a count says only who won.

When the majority is wrong

A settle over ballots cannot see a majority that is wrong, only a majority. Prelec, Seung and McCoy (doi:10.1038/nature21054) ask each voter one more thing: what share of the others will pick each option. A minority that knows better predicts the majority and votes against it, so the option whose actual share most exceeds its predicted share is the informed one; on questions where most people are confidently wrong, that rule recovers the truth where a majority and a confidence-weighted vote both fail. It is the second verb a panel runs when the question is hard: surprising reads the ballots and the forecasts and names the answer, or says that fewer than two voters forecast and it has nothing to add. Prediction polls of this shape score about as well as prediction markets on the same questions (Atanasov et al., doi:10.1287/mnsc.2015.2374).

Standing from the rows

Pairwise rows say who listens to whom; they do not say who stands high in the group. EigenTrust (Kamvar, Schlosser and Garcia-Molina, doi:10.1145/775152.775242) reads that off the same rows: normalise them, take the principal eigenvector, and pull toward a uniform pre-trust so nobody falls to zero and the iteration settles. A voter weighed by voters who are themselves weighed stands high; a row from a voter nobody weighs counts for little. reputation prints the standing; the seat shows it beside a settle so a reader sees not only where the group landed but whose word carried it.

Where the rows come from

In the tracker, rows are configuration. In the seat, rows are memory: the pack’s trust atoms, dated and supersedable, moved by ljos learn when an outcome shows who was right. This crate takes rows from anywhere as JSON and does not care which.

Outcomes are rare; most issues close without anyone saying which option was right. Dawid and Skene (doi:10.2307/2346806) estimate each voter’s accuracy without a truth, from how often it agrees with the answer the other voters make likely, by expectation maximisation. reliability runs that over a project’s settled issues, and ljos calibrate turns the accuracies into rows, so weights move from the tracker’s own history. The row a voter gets is its accuracy, which is the weight a linear opinion pool gives a source believed that reliable (Genest and Zidek, doi:10.1214/ss/1177013825). Acemoglu, Como, Fagnani and Ozdaglar (doi:10.1287/moor.1120.0570) show what a stubborn voter does to such a pool: with an anchor near one it never moves and pulls the rest, which is why a persona’s anchor is a parameter here and not a default.

The rules were measured where the truth is known (examples/synthetic_voters.rs): voters with accuracies drawn uniformly between 0.35 and 0.95, so some are worse than chance, answer two-way questions, and the group decides under each rule; twenty seeds, four hundred questions each. Nine voters: one voter one vote 0.820; the accuracies as linear weights 0.873; the accuracies as log odds (Nitzan and Paroush, doi:10.2307/2526438) 0.934 against 0.939 for the same weights from the true accuracies, the ceiling; Hedge from equal rows 0.831, because after enough misses every row sits on the floor and the settle is a count again; Hedge with a fixed share of recovery (Herbster and Warmuth, doi:10.1023/A:1007424614876) 0.877; and the online form of calibration, each voter’s smoothed record of hits and misses so far as log odds before every question, 0.929. Fifteen voters: 0.877, 0.936, 0.974, 0.976, 0.891, 0.937, 0.972. Log-odds weights reach within half a point of the ceiling whether estimated in one batch or kept as a running record; multiplicative shrinking does not, even with recovery. ljos calibrate writes log odds for that reason, and ljos learn keeps the record.

Seldon

Seldon is an opinion-dynamics engine that integrates the same models as ordinary differential equations. This crate can write its inputs and read its output so the discrete step can be checked against a second implementation. It does not link Seldon; it runs the binary when present.