Where Is the Truth When AI Agents Disagree? Dependence-Aware Belief Propagation for Unsupervised Truth Discovery (Extended Version)

Laure Berti-Equille

cs.AINov 3, 2026

Where Is the Truth When AI Agents Disagree? Dependence-Aware Belief Propagation for Unsupervised Truth Discovery (Extended Version)

Authors: Laure Berti-Equille

Organizations: IRD, ESPACE-DEV, Montpellier, France

Abstract

LLM agents often give conflicting answers to the same question, and many deployed agents are variants of one base model, so their errors are correlated. We study truth discovery among such agents: inferring the true answer and each agent's reliability without labels. Classical truth-discovery and crowdsourcing estimators reward an agreeing bloc and can fall below majority vote. We propose BP-TD, which adds per-agent decorrelation weights to mean-field variational inference on a one-coin Dawid-Skene model, so that agents sharing a base model count together as about one vote. Its first iteration is exactly a weighted vote; later iterations estimate agent reliability. With 13 local agents on MMLU, BP-TD beats majority vote without any labels (0.716 vs. 0.624 on 160 questions; 0.707 vs. 0.674 on 10,000) and ranks agents by their true accuracy, which classical estimators invert. The gain depends on the pool: over 2,852 sub-pools of four benchmarks, decorrelation helps when the largest correlated bloc is weaker than the other agents and hurts when it is the strongest, and we found no label-free statistic that tells the two cases apart. Labels change the picture quickly: with 20 labelled questions, selecting the single best agent is more accurate than every aggregator we tested on MMLU, ARC and TruthfulQA.

Figures & tables

Fig. 1: The agent–question–value graph and the two messages of BP-TD. An edge links an agent to the value it asserts on a question. Truth update (agents

\to

questions, Eq. 1): each agent sends its weighted vote

w_{a}\,\mathbb{E}\log r_{a}

to the value it chose. Reliability update (questions

\to

agents, Eqs. 2–3): each agent receives the current belief in the values it asserted, which updates its Beta reliability. Dashed box: a dependence group (agents on one base model); each member’s vote is scaled by

w_{a}

, so the group counts as about one vote.

Agent	Base model	Type	MMLU	SciQ	TQA	ARC
direct:qwen2.5:14b	qwen2.5	direct	0.825	0.988	0.810	0.919
direct:qwen2.5:7b	qwen2.5	direct	0.762	0.981	0.740	0.906
rag:qwen2.5:7b	qwen2.5	RAG	0.762	0.975	0.740	0.906
sc:qwen2.5:7b	qwen2.5	self-cons.	0.756	0.981	0.740	0.906
sc:llama3.2:latest	llama3.2	self-cons.	0.487	0.950	0.520	0.744
rag:llama3.2:latest	llama3.2	RAG	0.472	0.969	0.520	0.731

TABLE I: Agent pool: base model, agent type, and accuracy per dataset (measured on gold, on answered questions). OpenClaw never answers.

Method	MMLU ( $160$ )	SciQ ( $160$ )	TruthfulQA ( $100$ )	ARC ( $160$ )
Majority vote (MV)	0.624	0.969	0.650	0.847
BP-TD cooccur, $\theta$ val.-tuned	0.751 + [12]	0.969 [92]	0.629 [14]	0.842 [18]
one-pass = weighted vote	0.715 +	0.969	0.622	0.843
BP-TD cooccur, $\theta{=}0.5$ (no labels)	0.716 +	0.969	0.615	0.832
BP-TD cooccur, Otsu $\theta$ (no labels)	0.713 +	0.961	0.617	0.843
BP-TD family (no labels)	0.716 + [11]	0.976 [9]	0.586 [11]	0.879 [11]

TABLE II: Accuracy on the test halves, mean over

40

splits. + / - : significantly above/below majority vote (Nadeau–Bengio corrected resampled-

t

, Holm-corrected within the dataset). [

n

]: mean number of iterations of loopy BP-TD; rows marked one-pass use one iteration. CARE, ISP and OW-I were run on the same splits in a separate pass (Holm family of

7

). Bold: best aggregator per column (the best-agent row uses labels and is excluded).

Fig. 2: (a) Gain of loopy BP-TD cooccur over majority vote as a function of

\theta

(full sets); stars mark the label-free Otsu

\theta

. (b) Gain of BP-TD family over majority vote across sub-pools. Dark: random sub-pools whose largest base-model group is not the most accurate group; light: sub-pools whose largest group is the most accurate (random and constructed). (c) Gain of the best agent selected on

k

labelled questions (solid) against label-free BP-TD family (dashed,

k{=}0

); mean over

40

draws.

Fig. 3: Estimated vs. true per-agent reliability on MMLU. BP-TD-cooccur recovers the ranking (Spearman

\rho{=}{+}0.94

); Dawid–Skene inverts it (

\rho{=}{-}0.62

). Dashed lines are least-squares fits.

Method	$5{,}000$ questions	$10{,}000$ questions
Majority vote	0.681	0.674
BP-TD cooccur, $\theta$ val.-tuned	0.755 + (+0.074)	0.748 + (+0.073)
one-pass = weighted vote	0.755 + (+0.073)	0.744 + (+0.069)
BP-TD cooccur, $\theta{=}0.5$	0.710 (+0.029)	0.702 + (+0.028)
BP-TD cooccur, Otsu $\theta$	0.737 (+0.056)	0.715 (+0.040)
BP-TD family	0.718 + (+0.036)	0.707 + (+0.032)

TABLE III: MMLU at scale (vLLM, half precision): accuracy on the test halves, mean over

10

splits, gain over majority vote in brackets. Marks as in Table II .

Fig. 4: Scalability (synthetic). (a) log–log runtime vs.

n\cdot m

; (b) agent-axis sweep (

n{=}1000

) exposing the

O(m^{2})

term.

Fig. 5: BP-TD’s accuracy gain over majority vote vs. per-question agent disagreement (

1-

majority share), stratified into quartiles within each dataset (single held-out split). The gain rises with disagreement on MMLU, is non-positive throughout on TruthfulQA, and is flat on SciQ.

Fig. 6: Controlled correlated-bloc stress test on the real ARC answers: we append

k

synthetic agents sharing one wrong answer per question and sweep

k

at fixed hyperparameters, under (a) shared and (b) distinct bloc provenance (

\uparrow

better). Curves: majority vote (MV) and four BP-TD variants (cooccur, family, shared-err, none). Mean

\pm

SD over

20

injections.

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Believed but Not Said: Measuring Hidden Belief Collapse in Multi-Agent LLM Discussions

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LLM systems increasingly rely on groups of agents that discuss, critique, and check one another, assuming that peers will catch individual errors. We test this assumption against a minimal adversary. In a ten-agent factual discussion, one or three adversarial agents repeatedly assert a plausible false answer. After each round we probe each benign agent's private answer through a separate call whose response is hidden from its peers, and we separately label its public stance toward the claim. Across six models and three factual-QA datasets, groups remain stable without an attacker: only 0.6% of benign agents finish with the false answer. A single adversarial agent increases this rate to 44.8% and three to 60.5%. Studies of conformity typically report public agreement without private change; we find the reverse. With three adversarial agents present, benign agents hold the false answer in 51.6% of exposed turns but publicly endorse it in only 19.7%. Much of the influence therefore remains invisible in the discussion, and the false answers persist when agents are asked for their own views. Agents that retain the true answer often fail to defend it; once adopted, the false answer spreads among benign agents, and baseline knowledge does not predict robustness.

Abstract

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