Consensus is Strategically Insufficient: Reasoning-Trace Disagreement as a Knowledge-Representation Signal

Abstract: Multi-agent systems are commonly designed to reduce disagreement through voting, consensus protocols, debate, or fault-tolerant aggregation. We argue that this objective is insufficient for value-laden tasks, where disagreement may reflect genuine normative uncertainty rather than agent error. Building on prior work on reasoning-trace disagreement in human-AI collaborative moderation, we propose a knowledge-representation layer in which reasoning traces and agent decisions are abstracted into symbolic disagreement states. Given agents producing explicit reasoning traces and binary decisions, we distinguish four states according to reasoning similarity and conclusion agreement: convergent agreement, divergent agreement, convergent disagreement and divergent disagreement. These states support defeasible strategic routing rules. We instantiate the framework in content moderation and argue that disagreement-aware routing provides a bridge between sub-symbolic LLM deliberation and symbolic knowledge representation for multi-agent strategic reasoning.

• The paper introduces a four-state taxonomy combining reasoning similarity and decision agreement to classify cases as convergent agreement, divergent agreement, divergent disagreement, or convergent disagreement.
• The paper maps each state to defeasible actions—automate, automate with explanations, seek context, or escalate—so systems can respond strategically instead of relying only on majority votes.
• The paper’s evaluation on 600 hate-speech cases found that the taxonomy tracked human disagreement, with convergent disagreement strongest, and outperformed divergence magnitude alone in precision and F1 for identifying contested cases.

Motivation: disagreement as signal, not noise

The paper's central argument targets a design assumption shared by most LLM-based multi-agent architectures: that inter-agent disagreement is a transient defect to be eliminated through majority voting, debate rounds, or Byzantine-tolerant aggregation. The authors contend this assumption is defensible for instrumental tasks, where disagreement typically indicates noise or reasoning failure, but fails for value-laden tasks such as content moderation, where disagreement can be a stable property of the decision problem itself, reflecting genuine normative pluralism rather than agent error. The work extends the authors' prior study on reasoning-trace disagreement in human-AI collaborative moderation (2606.04223) by adding a knowledge-representation (KR) layer that turns disagreement structure into a symbolic, actionable state.

The reframing is architectural rather than merely diagnostic: instead of asking how agents can be made to agree, a disagreement-aware controller asks what the structure of disagreement implies about the appropriate next action — whether to decide, inquire, or escalate. This transfers the perspectivist stance from NLP datasets, where annotator disagreement is treated as informative (Kennedy et al., 2020), to system design.

The four-state taxonomy

The formal model considers $n$ agents, each producing an output $\langle r_i, d_i, v_i, \gamma_i \rangle$ for a case $c$: an explicit reasoning trace $r_i$, a binary decision $d_i \in \{Keep, Remove\}$, a perspective profile $v_i$, and a confidence score. Two relations define the vocabulary. Reasoning similarity is the mean pairwise cosine similarity $\overline{sim}(c)$ of embedded traces, thresholded at $\theta_s$; conclusion agreement is the maximal decision share $p^*(c)$, thresholded at $\theta_a$. Crossing the two binary dimensions yields four symbolic states:

State	Definition	Interpretation
Convergent agreement (CA)	High similarity, agreement	Easy case for automation
Divergent agreement (DA)	Low similarity, agreement	Robustness via independent reasons
Divergent disagreement (DD)	Low similarity, disagreement	Ambiguity or unstable interpretation
Convergent disagreement (CD)	High similarity, disagreement	Candidate signature of value conflict

The load-bearing conceptual claim concerns $\langle r_i, d_i, v_i, \gamma_i \rangle$0: when agents reason similarly but conclude differently, residual disagreement plausibly reflects different value weightings over a shared case description rather than divergent interpretation. Forcing consensus here, the authors argue following Denisov-Blanch et al. (Denisov-Blanch et al., 20 Feb 2026), may conceal rather than resolve a normative conflict. Both thresholds are explicitly acknowledged as policy parameters rather than semantic boundaries, and reasoning traces are treated as observable justificatory artifacts, not formal proofs — a concession that bounds the strength of any claim about logical equivalence of traces.

Defeasible strategic routing

Each state maps to a default meta-action via nonmonotonic rules in the spirit of Brewka et al.: $\langle r_i, d_i, v_i, \gamma_i \rangle$1; $\langle r_i, d_i, v_i, \gamma_i \rangle$2 (preserving explanation diversity for different stakeholders); $\langle r_i, d_i, v_i, \gamma_i \rangle$3; $\langle r_i, d_i, v_i, \gamma_i \rangle$4. The defeasible structure is essential: any rule can be overridden by domain constraints, e.g., $\langle r_i, d_i, v_i, \gamma_i \rangle$5 even under $\langle r_i, d_i, v_i, \gamma_i \rangle$6, or $\langle r_i, d_i, v_i, \gamma_i \rangle$7 even under $\langle r_i, d_i, v_i, \gamma_i \rangle$8. The authors frame the choice decision-theoretically: automation risks illegitimate decisions, context-seeking adds latency, and escalation consumes scarce institutional capacity — the disagreement state serves as a structured signal for allocating these costs. Notably, the $\langle r_i, d_i, v_i, \gamma_i \rangle$9 asymmetry is presented as the taxonomy's chief benefit: both states involve disagreement, yet call for opposite strategies (escalation versus information acquisition), a distinction a vote-counting aggregator cannot express.

Empirical faithfulness check

Because the routing framework is normative, the authors run a sanity check asking whether the abstraction $c$0 tracks epistemic situations that humans also find distinct. Five LLM agents from the same base model are differentiated only by system prompts encoding five moderation perspectives (harm-focused, context-sensitive, community-norms, free-expression, legal-framework), isolating value-profile differences from capability differences. They evaluate on 600 items from the Measuring Hate Speech corpus (Kennedy et al., 2020), stratified by human annotator disagreement.

The conceptually predicted ordering of mean human annotator disagreement, $c$1, is preserved:

State	$c$2	Mean human disagreement $c$3
DA	118	0.351
CA	24	0.638
DD	382	0.751
CD	76	0.782

The two disagreement states are jointly separated from the two agreement states with Cohen's $c$4 ($c$5, $c$6). Against a magnitude-only baseline using $c$7, category-based routing achieves higher precision (0.401 vs. 0.347) and F1 (0.548 vs. 0.503) for flagging high-human-disagreement cases, while the divergence-only predictor attains higher recall (0.915) but low precision — it flags many cases where agents reason differently without corresponding human disagreement. The authors are explicit that the load-bearing result is qualitative (the ordering and the agreement/disagreement gap), not the F1 figures, which are modest in absolute terms.

Limitations and open questions

The paper concedes several constraints at the point where they bear on the results. The empirical check uses a single corpus, a single domain, and embedding-based similarity as a coarse proxy for reasoning equivalence; prompt-based perspective differentiation may underrepresent the heterogeneity of genuinely independent agents, and all agents share one base model. The routing rules are hand-designed defaults rather than learned or formally verified policies. The authors accordingly frame the evaluation as a faithfulness check on the KR layer, not a benchmark of routing quality. Open questions they identify include: whether the four-state structure replicates in domains such as medical triage and legal assistance; whether coupling traces to explicit argumentation graphs would detect support, attack, and undercutting relations directly rather than via embedding similarity; and whether explicit cost models would permit game-theoretic analysis of escalation choices.

Conclusion

The paper reframes disagreement in LLM-based multi-agent systems from an aggregation obstacle into a representable epistemic state, providing an explicit interface between sub-symbolic deliberation and symbolic strategic control. Its two-axis taxonomy — reasoning similarity crossed with conclusion agreement — yields defeasible routing rules that decide not only what to conclude but whether to decide at all. The preliminary empirical result, that the structural abstraction predicts human disagreement better than trace-divergence magnitude alone and that convergent disagreement most strongly tracks human normative conflict, is consistent with the central thesis while remaining, by the authors' own account, an early sanity check rather than a definitive validation.