Counting Moves, Weighing Voices: Bayesian Dialectical Argumentation for Calibrated Multi-LLM Councils under Persistent Adversaries

1 Introduction

• Existing aggregators can mistake decisiveness for correctness: unanimous councils are wrong 18% of the time, and evaluated graded-confidence methods have ECE above 0.15, with MoA’s near-constant scores an exception.Against persistent persuasive adversaries, plurality can collapse toward chance, MoA can be captured, and some resistant methods avoid consulting the council.Source: §1 · p. 1
• BDA treats protocol-governed Propose, Challenge, and Concede moves as per-agent observations in a classical annotator model with learned reliability.The formulation extends to K>2 using a tempered composite likelihood and per-agent confusion matrices.Source: §1 · pp. 1–2
• When a fitted agent reliability falls below chance, BDA gives that agent negative weight, so its endorsement becomes evidence for the opposite answer rather than merely another vote.The method requires no additional model calls; the introduction also reports a reproducibility pipeline over cached traces and a $220 campaign.Source: §1 · pp. 1–2
• ECE 0.016 makes BDA per-agent the best-calibrated free aggregator; it improves plurality’s decision by 1.7 points, while reliability weighting wins attack accuracy on two of three domains.Under attack, the stacker wins positional-K>2 accuracy, while reliability weighting wins binary and semantic-K>2 accuracy.Source: §1 · p. 2, Figure 1 · p. 2

Multi-LLM councils

• Multi-LLM aggregation methods use varied mechanisms, while prior studies report fragile gains, poorly calibrated confidence, conformity effects, and the importance of the full interaction trajectory.The paper uses MoA-family methods and plurality as baselines.Source: §2 · p. 2

Argumentation-based verification

• Argumentation-based verification scores argument strength, but ArgLLMs uses a margin as confidence and relies on argument mining and judging that can themselves be unreliable.BDA instead uses typed moves with public, verifiable communication semantics.Source: §2 · p. 2

Reliability-weighted aggregation and calibration

• BDA carries classical reliability-weighted voting and annotator models onto typed deliberation, adding per-agent priors, K-candidate inference, and adversarial evaluation.The related-work discussion identifies label-switching ambiguity in unsupervised estimation as the issue a supervised prior resolves.Source: §2 · pp. 2–3

3 Bayesian Dialectical Argumentation

• The method reduces deliberation to who endorsed which answer, discarding prose; at K=2, rounds barely affect the final decision, while dialectics improves the reliability estimator.The reported estimator ECE changes from 0.117 to 0.080; the contribution to the final decision grows with K, with fix/break changing from 1.10 to 1.61.Source: §3 · p. 3
• A trace records typed moves with agent identity, round, and relevant answer or target; Propose, Challenge, and Concede are the protocol’s experimental move types.A proposal endorses its answer, a concession endorses the other proposal’s answer, and a challenge rejects its target’s answer; abstentions and self-concessions carry no information.Source: §3 · p. 3
• For each candidate truth, BDA counts each agent’s consistent and inconsistent informative moves, models latent reliability with a Beta prior, and integrates it to obtain closed-form evidence.The posterior yields both the maximizing answer and its probability as confidence, using log-space operations without language-model calls.Source: §3 · p. 3
• The per-agent model fits seat reliability on labeled calibration folds and pools it into a prior; about 25 labels suffice, and all supervised comparison arms receive the same budget.The profile is fitted once and amortized across deployment; setting κ=0 recovers the shared prior.Source: §3 · p. 3
• For K>2, BDA’s general model gives each agent a confusion matrix over candidate answers, with a tempered composite likelihood and cross-validated hyperparameters.At K>2, a challenge counts in multiple rival cells, making the counts pseudo-observations; calibration is therefore cross-validation-earned rather than guaranteed by construction.Source: §3 · pp. 3–4
• At K=2, BDA’s decision is a Bayes-optimal weighted majority: log-odds reliability weights become negative for agents whose reliability is below chance.Plurality is the equal-positive-weight special case; the more general confusion model retains an additive committee rule without the same optimality claim.Source: §3 · p. 4

4 Properties

• BDA confidence is calibrated when its prior and likelihood match the data-generating process; for K>2 with challenges, the composite-likelihood model instead relies on cross-validated correction.The confusion model’s calibration is not guaranteed by construction, even at τ=1.Source: §4 · p. 4
• At K=2, finite-strength integration can cap the posterior below one, and a symmetric prior can leave it unchanged; these binary artifacts dissolve for K>2.The K>2 one-coin model can become overconfident, while the confusion model’s temperature absorbs the growth; the ceiling is specific to the finite-strength construction.Source: §4 · p. 4
• Rewriting self-reported move confidences does not change the posterior, including across the reported permutation of confidences over 4,500 traces.An adversary that changes what moves endorse is a separate concern.Source: §4 · p. 4
• Prior sensitivity depends on the regime: at the uniform-error K=2 ceiling it does not vanish with more evidence, while the K>2 confusion-model prior washes out at O(λ/Ni).The prior dominates only in the sparse regime.Source: §4 · p. 4
• Under light contamination, the confusion model’s off-diagonal errors can be underdetermined, so the fewer-parameter one-coin model can recover faster.The misspecified prior is damped but not always forgotten; the confusion model’s prior washes out with evidence.Source: §4 · p. 4
• Reliability weighting requires unreliability to be identifiable in calibration, stationary into deployment, and attached to a stable seat; rotation defeats per-seat identification.A sleeper that behaves well during calibration inherits trust until refitting catches the change.Source: §4 · pp. 4–5

Experimental data and council

• The study uses three binary datasets with 500 examples each, PubMedQA with 300 balanced examples, and a 500-example four-way MMLU subset, across three seeds.The primary council runs three rounds: an initial proposal followed by two rounds of proposals, concessions, and challenges; every aggregator sees the same traces.Source: §5 · p. 5

Compared aggregators

• Baselines span plurality, deliberation synthesis, argument verification, discriminative stacking, gated voting, and unsupervised Dawid–Skene estimation; BDA is tested in three variants.Baseline evaluators and synthesizers use a stronger model than any council seat, and MoA-family confidences are near-constant.Source: §5 · p. 5

Model selection

• Supervised aggregators share a 25-label budget, with nested leak-free cross-validation selecting hyperparameters on Brier score.Outer folds produce reported numbers; inner folds select hyperparameters, and no test label influences a choice that scores it.Source: §5 · p. 5

What BDA does not win

• With baselines given the same label budget, leak-free isotonic recalibration collapses everyone’s calibration error; recalibrated ArgLLMs then leads on Brier, atop its accuracy lead.On clean data, BDA is the only free arm with a decision gain and no recalibration stage.Source: §6 · p. 5

Clean K>2 results

• On PubMedQA and MMLU, one-coin BDA has ECEew 0.30 and 0.18 versus plurality’s 0.26 and 0.09; tempering repairs calibration with accuracy within a point.A single cross-validated temperature also recovers calibration because multiple moves from one seat per task are correlated and otherwise over-counted.Source: §6 · p. 5
• The confusion model’s tempered posterior reaches ECEew 0.072 on PubMedQA and 0.063 on MMLU at zero cost; a one-coin model with one CV temperature reaches 0.051 and 0.037.The confusion matrix is held in reserve for attack settings, where systematic coalition errors can be inverted; deliberation’s net value rises with K (fix/break ratios 1.10, 1.20, 1.61).Source: §6 · pp. 5–6

Clean binary results

• BDA per-agent leads free-arm calibration at ECEew 0.016 versus majority’s 0.160 and beats plurality by ∆Acc +0.017; ArgLLMs leads accuracy and pays per task.The decision-gain confidence intervals are [+0.010, +0.024] for both pooled and question-clustered estimates.Source: §6 · p. 5, Table 2 · p. 6

Threat model

• The threat model distinguishes persistent bad seats, including during calibration, from attackers rotating to fresh seats each task; live adversaries are compliance-measured at 87–100% anti-correct proposals.The live attack has adversarial seats argue against truth, select defensible wrong answers, concede to allies, and blend in.Source: §7 · p. 6

Dose–response

• With a persistent synthetic adversary, BDA per-agent rises to 0.923/0.915 at pwrong=1 from 0.751 clean, while majority falls to 0.163.The dose-response isolates inversion under persistence; rotation is a different regime.Source: §7 · p. 6

Live coalition results

• Under the live coalition, confusion leads binary and PubMedQA while stacking leads MMLU; binary k=2 rises 0.734→0.892 and PubMedQA k=2 0.471→0.840 versus one-coin.The confusion model leads every PubMedQA cell and binary k=2; under seed-clustered bootstrap, binary k=2 is +0.027 and PubMedQA k=2 is +0.087 over the stacker.Source: §7 · pp. 6–7

Mechanism and permutation control

• The confusion model’s edge on PubMedQA depends on label identity, which permutation destroys; positional MMLU carries no such identity and favors the label-indifferent stacker.The control identifies the identity component of the confusion model’s margin over stacking.Source: §7 · p. 7

Role of deliberation

• Round-0-truncated traces are more accurate under attack than full traces; one-coin binary k=2 scores 0.933 versus 0.736, as later rounds import contagion.The result separates the round-0 reliability-weighted vote from the full deliberation trace’s role in estimation and calibration.Source: §7 · p. 7

Fair role-matched attack

• In a fair role-matched attack, Self-MoA collapses, ArgLLMs’ defense erodes as the answer space grows, and the council holds near clean with two of three seats adversarial.The figure reports K=2, 3, and 4 over full sets and three seeds, with seed-standard-deviation error bars.Source: §7 · p. 7

Further checks

• The live coalition can flip genuine seats through coordinated challenges, making the effective corrupted fraction exceed the nominal 2/3 at k=2; weak and near-chance swap-in seats degrade gracefully.At k=2, the effective corrupted fraction is 0.68/0.72; the confusion model still leads and remains calibrated.Source: §7 · pp. 6–7

Supported conclusions and non-claims

• The supported results are best-calibrated zero-cost confidence, a decision gain recalibration cannot produce, and leading accuracy under persistent attack on two of three domains.The stated non-claims include clean accuracy dominance, positional-K>2 attack dominance, post-recalibration calibration dominance, and unconditional robustness.Source: §8 · p. 7

Scope of the formulation

• BDA applies beyond LLM councils to repeated multi-agent decisions with protocol-typed, agent-attributed commitments over shared candidates and reliability estimable across tasks.The council is presented as one instantiation of that broader inference problem.Source: §8 · p. 7

Limitations and assumptions

• BDA needs labeled calibration data, about 25 labels amortized across deployment; label-free settings therefore exclude it.The compared baselines receive the same label budget.Source: §8 · p. 7
• The adversary must misbehave during calibration and remain unreliable; a sleeper inherits trust, while policy shifts cost the confusion model and stacker their entire edge.Periodic refitting mitigates sleeper exposure; the confusion model and stacker require persistent error structure.Source: §8 · p. 7
• Moderate-dose rotation defeats every trace-reading arm; near-homogeneous reliabilities reduce per-agent BDA to a noisier shared model, and move independence is an idealization absorbed by temperature.Abstention is untested.Source: §8 · p. 7

9 Conclusion

• BDA’s confusion refinement provides calibrated probabilities as the answer set grows and can discount or invert unreliable voices.The conclusion identifies aggregation-aware adversaries, online refitting, hierarchical and semi-supervised estimation, and temporal-logic verification as open directions.Source: §9 · p. 7

A Notation and Acronyms

• The notation appendix lists acronyms in order of first appearance and collects the paper’s symbols in Table 3.Source: A Notation and Acronyms · p. 9, Table 3 · p. 10

B Primer, Algorithm, and the Methods

• The primer gives the probability facts behind the model and an algorithm that assembles the posterior from per-agent factors in log-space over integer counts.Its categorical noise model assigns probability θ to a move pointing at the true answer and distributes the remaining probability over the K − 1 alternatives.Source: B Primer, Algorithm, and the Methods · p. 9

B.1 The methods, one by one

• The methods comparison includes label-free DS-EM, MoA and MoA-Lite synthesizers, and BDA variants with shared or per-agent reliability modeling.The supervised methods use the same 25 calibration labels through nested cross-validation; the BDA confusion model is tuned by cross-validation on Brier score.Source: §B.1 · p. 10

• A method reads the council when changing the deliberation trace can change its verdict; Self-MoA and ArgLLMs instead answer from private pipelines and are attack-invariant by construction.BDA, majority, and MoA read the council, though MoA uses members’ free-text surfaces rather than only typed moves.Source: §B.2 · p. 11
• The attack corrupts evidence generated inside each method’s own channel while keeping its aggregation rule fixed, so the comparison tests how the rule handles adversarial evidence.For council readers it targets two of three seats; for Self-MoA it targets the sampled model, and for ArgLLMs the argument generator.Source: §B.2 · p. 11
• At matched three-model architecture and attack fraction, MoA falls from 0.72 to 0.48 while BDA moves from 0.75 to 0.73, isolating a reliability-weighting comparison.Self-MoA and ArgLLMs’ collapses are separately attributed to their single-pipeline architectures, which lack a redundant channel.Source: §B.2 · p. 11
• The attack leaves synthesizers and evaluators clean, favoring those baselines, while the K>2 ArgLLMs attack is gold-routed to undermine the correct option and bolster wrong ones.The authors flag this per-option-optimal attack as stronger than the commit-to-one council adversary.Source: §B.2 · p. 11

C.1 Calibration

• When the assumed joint law generates the data, posterior probabilities are exactly calibrated; empirical ECE instead depends on cross-validating the prior.The theorem does not imply the reported empirical calibration.Source: §C.1 · p. 11

C.2 The weighted-majority form

• With one endorsement, BDA's binary MAP rule uses log-reliability odds; below-chance reliability gives negative weight, so adversary endorsements move odds toward rival answers.The live adversarial experiment reports fitted reliability around 0.18 at k=1 and 0.23–0.24 at k=2 for the corrupted seat.Source: §C.2 · p. 12

C.3 Consistency, ceiling, and collapse at K=2

• For K=2 with true reliability above 1/2 and α0>β0, MAP converges and error decays exponentially; symmetric priors leave the posterior equal to the prior.The posterior ceiling is a finite-strength construction choice; a growing-strength hierarchical reliability model would remove it.Source: §C.3 · p. 12

C.4 The ceiling and collapse dissolve for K>2

• For K≥3, unanimous evidence makes the posterior concentrate without a ceiling, and one informative move shifts it even under a symmetric prior.The authors note that clean K>2 data can also produce posterior over-concentration.Source: §C.4 · pp. 12–13

C.5 The confusion model and its uniform-error submodel

• The deployed K-candidate model uses per-agent confusion matrices and a tempered composite likelihood; with challenges at K>2, calibration is cross-validated, not guaranteed by the calibration theorem.The likelihood is exact only when every move expands to a singleton; correlated moves violate the conditional-independence idealization.Source: §C.5 · p. 13

C.6 Confidence invariance; C.7 Prior sensitivity

• Rewriting self-reported confidence leaves the posterior unchanged, while confusion-model prior influence at K>2 decays per agent as O(λ/Ni).The prior can still dominate in the sparse regime.Source: §C.6 · p. 14, §C.5 · p. 14

C.8 Numerical verification

• With a symmetric Beta(1, 1) prior, unanimous endorsements leave the K=2 posterior at its prior for every N but make it concentrate for K>2.Permuting confidence values across 4,500 binary traces changed no posterior; the weighted-majority implementation matched the rule exactly on random single-endorsement instances.Source: §C.8 · p. 14

D.1 Leak-free nested selection; D.2 Run variance; D.3 Scoring pitfall: extracting a committed answer

• Nested five-fold selection uses held-out outer folds and inner Brier tuning; three seeds address stochastic serving, while a cached judge recovers prose-only commitments and leaves genuine noncommitments wrong.The faithful ArgLLMs multi-option dispatch returns canonical option labels, with a 100% parse rate.Source: §D.1 · p. 14, §D.2 · p. 14, §D.3 · p. 15

D.4 Implementation pitfall: the faithful multi-option baseline

• Faithful multi-option ArgLLMs verifies the task's own candidate options, restoring 100% parsing and council-invariance; clean accuracy rises on PubMedQA but falls on MMLU versus the flawed wrapper.The wrapper's proposer-paragraph candidates introduced parsing errors and made ArgLLMs appear attackable on K>2.Source: §D.4 · p. 15

D.5 Design pitfall: the vocal adversary

• A vocal adversary that re-proposes about 2.9 times per task can inflate per-move evidence, producing 0.996 BDA accuracy; natural one-move deliberation removes the volume artifact.Full-trace and one-vote-per-agent analyses agree for the stealthy adversary.Source: §D.5 · p. 15

D.6 Scoring pitfall: degenerate ties under attack

• Under live k=2 PubMedQA attacks, seeded-random tie-breaking raises stacker accuracy from 0.643 to 0.75 by removing a lexicographic tie artifact.The artifact arose when identical candidate feature rows tied and lexicographic ordering correlated with wrong-answer choices.Source: §D.6 · p. 15

D.7 Implementation, storage, and cost

• Cached traces make aggregators pure functions of identical inputs, while a canonical numbers file and independent verifier support reproducible checks; BDA aggregation itself has zero marginal cost.The full campaign cost about $220 at list prices; post-hoc comparisons over cached traces have zero marginal cost.Source: §D.7 · p. 16

E.1 Headline with both binnings and recalibration

• BDA's clean binary posterior tracks the reliability-diagram diagonal, and its calibration advantage is uniform across nine dataset-seed cells; equal-budget isotonic recalibration closes calibration gaps and re-derivation leads Brier and accuracy.BDA's clean claims are its zero-added-cost calibration and decision gain; recalibration does not produce that decision gain.Source: Figure 4 · p. 16, Figure 5 · p. 16, §E.1 · p. 16

E.2 Ablations

• Per-agent reliability and an estimator using all informative moves are the winning ablation choices; transfer beats majority on ECE and Brier across all three held-out datasets.On TruthfulClaim, per-agent accuracy is 0.791 against 0.779, with ECE 0.096 against 0.131.Source: §E.2 · pp. 16–17, Table 7 · p. 17

E.3 Self-reported confidence, and the best member

• BDA per-agent reaches ECE 0.016 and improves accuracy over plurality by 1.7 points, while its accuracy advantage over the leak-free best member is a statistical tie.BDA’s ECEew is 0.016 versus 0.067 for the best member; the reported accuracy difference is +0.006 with 95% CI [−0.004, +0.016].Source: Table 6 · p. 17, §E.3 · p. 18

E.4 Clean K>2; E.5 What fixes clean K>2: temperature, not the matrix

• On clean K>2 tasks, tempering repairs the one-coin model’s over-confidence without changing accuracy; the confusion model improves ECEew from 0.304 to 0.072 on PubMedQA and 0.183 to 0.063 on MMLU.The selected temperature, rather than the learned confusion matrix, supplies this clean-data calibration fix.Source: §E.5 · p. 18, §E.4 · p. 18, Table 9 · p. 18

E.6 Label efficiency of the supervised family

• About 25 calibration labels reach the supervised arms’ plateau, and the confusion model’s K>2 calibration advantage is already present at that budget.On PubMedQA at n=25, its ECEew is 0.091 against 0.355 for the one-coin model.Source: §E.6 · p. 19, Table 11 · p. 20

F.2 The stealthy coalition adversary; F.3 Dose–response (synthetic), full grid

• Under a persistent synthetic adversary, per-agent BDA first dips near chance then improves as its fitted weight turns negative; under rotation, the confusion model recovers at high corruption dose.At pwrong=1 with a persistent k=2 coalition, the confusion model reaches 0.947; under rotation it reaches 0.811 at pwrong=1.Source: §F.3 · p. 19, §F.2 · p. 19, §F.1 · p. 19

F.4 Live attack: calibration under fire; F.5 Rounds under attack: the gain is round-0 weighting

• Round-0 reliability weighting is more accurate than full-trace aggregation in 11 of 12 attacked cells, while the tempered confusion posterior has ECEem 0.045–0.109 across six cells.The authors attribute the attacked-decision loss from later rounds to coalition challenges flipping genuine seats; the typed trace still contributes to reliability estimation and calibration.Source: §F.5 · p. 19, §F.4 · p. 19, Table 14 · p. 20

F.6 Invariance checks

• ArgLLMs and Self-MoA are invariant to the attack in the faithful multi-option dispatch, whereas BDA’s live-attack accuracy depends on council evidence.ArgLLMs’ clean multi-option confidence is already poorly calibrated.Source: §F.6 · p. 20

F.7 The fair attack, in full

• Under the fair attack, BDA stays near its clean accuracy while Self-MoA collapses and ArgLLMs loses 24–28 points; at full corruption, every method fails.The attack targets two of three council members with the same anti-correct role used inside each comparison method.Source: §F.7 · p. 21

F.8 The sleeper: a contamination axis

• With a pure sleeper, per-agent BDA falls to 0.17 accuracy, but reaches 0.45 once 20% of the calibration window contains the turn and 0.72 when fully aware.The learned vote weight flips negative after the seat’s fitted reliability crosses the council mean.Source: §F.8 · p. 21, Figure 7 · p. 21
• At light contamination, one-coin recovers faster than confusion (0.45 versus 0.26 at f=0.2), but confusion overtakes from f≈0.6 and reaches 0.90 at f=1.No arm dominates the entire axis because cross-validation within the contaminated window cannot see the deployment shift.Source: §F.8 · p. 21, Figure 7 · p. 21

F.9 Recalibration erases the calibration edge, not the accuracy

• Leak-free isotonic recalibration equalizes clean-data calibration, but under attack it cannot restore accuracy when a vote is wrong.Recalibrated majority reaches ECEew≈0 under attack while achieving only 0.37/0.21/0.43 accuracy; BDA confusion reaches 0.89/0.84/0.72.Source: §F.9 · p. 21, Table 15 · p. 22

F.10 Unsupervised Dawid–Skene and label switching

• With a k=2 coalition, unsupervised DS–EM’s deployable initialization selects the coalition’s mirror mode; on MMLU it agrees with the coalition vote on all 1,500 tasks.The correct anti-mode is unreachable without labels, and the K>2 failure is mode capture rather than the exact K=2 label-switching symmetry.Source: §F.10 · p. 22, Table 16 · p. 22

F.11 The semantic/positional mechanism: label permutation

• Randomly permuting candidate labels costs the confusion model 0.100 on live PubMedQA k=2, but changes MMLU by only −0.005.The PubMedQA loss equals its margin over the stacker, while the confusion model’s +0.26 over one-coin remains.Source: §F.11 · p. 22, Table 17 · p. 22

F.12 Structure stationarity: the wrong-answer policy shift

• Across wrong-answer policies, confusion and stacker lose their learned-structure edge, while one-coin remains policy-robust in every shifted cell.The one-coin needs below-chance behavior to persist; confusion also needs the structure of which wrong answers the seat favors to persist.Source: §F.12 · pp. 22–23, Table 18 · p. 23

F.13 The monitoring result: row drift announces the change; F.14 Contagion and the weak seat

• Row drift exceeds twice its clean noise floor when 20% of the window contains the turn, before confusion accuracy recovers; attacked rounds also flip genuine seats and increase corrupted evidence beyond the nominal k/I.The drift is 0.074 against a floor of 0.033 at f=0.2; on k=1 cells, contagion raises the effective corrupted fraction from 0.33 to 0.44–0.59.Source: §F.13 · p. 23, §F.14 · p. 23, Table 19 · p. 23

G Qualitative Traces and a Worked Example

• The qualitative section moves from single-task traces to a worked example intended to make a BDA verdict reproducible by hand.Source: G Qualitative Traces and a Worked… · p. 23

G.1 An adversarial trace, end to end

• Fitted reliabilities of 0.21 and 0.29 give the two adversarial seats different negative weights, while the genuine seat’s reliability of 0.60 yields a positive weight.The more reliably wrong adversary receives the more negative weight; Table 20 attributes the per-agent log-likelihood contributions.Source: §G.1 · pp. 23–24, Table 20 · p. 24
• Majority voting returns False, but BDA returns True at 0.89, with inverted adversarial endorsements carrying 67% of the winning log-odds despite a genuine seat’s flip.If every seat argued False consistently for three rounds, the posterior would saturate toward 1.00 under strong evidence.Source: §G.1 · p. 24, Table 20 · p. 24

G.2 Coalition capture of a synthesizer (MMLU,

• On the MMLU example, majority voting and MoA return the coalition’s wrong answer B, while BDA returns the correct answer A; across this seed and condition, BDA is correct where MoA is fooled on 57 MMLU and 74 PubMedQA tasks.The genuine member flips under coalition pressure in the trace; elsewhere, some flips reflect honest difficulty rather than persuasion.Source: §G.2 · p. 24

H Small Open-Weight Council (Full)

• On the clean small council, per-agent wins on binary tasks (∆Acc +0.009, pwin=0.96), while plurality leads K>2 and tempered confusion improves ECEew to 0.033/0.050 against plurality’s 0.285/0.157.With near-chance, near-homogeneous reliabilities on K>2 tasks, there is no per-seat accuracy signal; the calibration repair does not require heterogeneity.Source: H Small Open-Weight Council (Full) · p. 24, Table 21 · p. 25

I Every Prompt, Verbatim

• The adversarial prompt commits a seat to arguing against the correct answer, while later rounds require typed Propose, Challenge, or Concede moves based on prior moves.The prompt describes this as an anti-answer role rather than a fixed-wrong answer; confidence uses epistemic and agreement rubrics.Source: I Every Prompt, Verbatim · pp. 24–25

J Provenance: Adopted versus New

• Abstention by adding “unknown” to K is unimplemented, and MArgE is excluded from the evaluation on cost grounds.Table 22 distinguishes prior-work baselines, building blocks, and evaluation targets from contributions new to the paper.Source: J Provenance: Adopted versus New · p. 26, Table 22 · p. 27