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arxiv: 2605.25929 · v2 · pith:6BJ6FVG7new · submitted 2026-05-25 · 💻 cs.MA · cs.LG

Multi-Agent Systems are Mixtures of Experts: Who Becomes an Influencer?

Pith reviewed 2026-06-29 19:24 UTC · model grok-4.3

classification 💻 cs.MA cs.LG
keywords multi-agent systemsLLM deliberationopinion dynamicsmixture of expertsinfluence mechanismsFriedkin-Johnsen modelagent competence
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The pith

Multi-agent LLM deliberation functions as an input-dependent mixture of experts

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The authors apply the Friedkin-Johnsen model of opinion dynamics to multi-agent large language model systems. They demonstrate that the model's parameters for stubbornness and influence are not fixed but instead depend on the particular input being processed. This input dependence effectively makes the multi-agent system behave like a mixture of experts, where different agents exert more influence on different tasks. If true, this means such systems can achieve better performance than either a single agent or a static combination of agents, provided that the influence is allocated according to each agent's competence on the given input. The work then explores how observable factors such as an agent's self-assessed confidence and initial alignment with others determine who becomes influential.

Core claim

The Friedkin-Johnsen parameters governing multi-agent deliberation are input-dependent, which recasts multi-agent systems as mixtures of experts capable of outperforming single agents and static ensembles when the routing of influence aligns with agent competence.

What carries the argument

Friedkin-Johnsen opinion dynamics, a model that tracks how individual stubbornness and interpersonal influence shape opinion updates over time in a group.

Load-bearing premise

The Friedkin-Johnsen model accurately represents the deliberation and opinion change processes observed in groups of large language models.

What would settle it

A direct measurement showing that the effective influence exerted by each agent in a multi-agent LLM discussion does not change as a function of the input topic or question.

Figures

Figures reproduced from arXiv: 2605.25929 by Franka Bause, Jonas Niederle, Martin Pawelczyk, Rebekka Burkholz.

Figure 1
Figure 1. Figure 1: FJ induces MoE. (a) FJ parameter variability across MMLU-Pro questions for GPT-5.4 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Association of competence and confidence for ChatGPT-5.4 Mini on MMLU-Pro. Hard routing towards the most competent agent. As a special case, we can also consider hard routing, where a single agent j ′ (S) receives all weight, leading to the condition E hPn j=1 aj rj (S) − rj ′(S)(S) i > E[Da(S)], because the local diversity Dπ(S)(S) = 0. Thus, hard routing must compensate for the diversity benefit with a s… view at source ↗
Figure 3
Figure 3. Figure 3: Example: Initial beliefs of agents (left). FJ weight matrix, [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Influence (mean ± 95% confidence interval) for different communication styles, differences in influence suggest perceived confidence plays a role in FJ dynamics. We empirically study the FJ dynamics in agentic sys￾tems and investigate how the routing weights are dependent on the different variables. If not indicated otherwise, the plots show results from the MMLU￾pro dataset with communication style prompt… view at source ↗
Figure 5
Figure 5. Figure 5: Logistic regression coefficients clas￾sifying the most influential agent. Confidence and competence are the strongest positive pre￾dictors. Communication styles coefficients suggest perceived confidence plays a role in FJ dynamics. Confidence leads to influence. To understand the routing behavior, we investigate the relation between metrics of the initial beliefs and competence with in￾fluence of agents by… view at source ↗
Figure 6
Figure 6. Figure 6: Parameter variability over all samples no special prompts for [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Parameter variability over all samples no special prompts for [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Confidence vs. Influence (left) and confidence vs. peer influence (right) with no special [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Confidence vs. Influence (left) and confidence vs. peer influence (right) with no special [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Probability of changing answer to the majority answer for cases where the agent is [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Results for GPT-5.4 Mini on the MMLU-Pro dataset. Roles seem to have an even bigger influence on perceived confidence as seen by the weights agents receive from the others. 22 [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Results for Qwen2.5-14B-Instruct on the MMLU-Pro dataset. The same tendencies as for GPT-5.4 Mini can be seen. confidence competence student teacher mathematician doctor rookie Rel. Confidence Alignment Alignm. Score Alignm. Count 0.0 0.1 0.2 0.3 Gini Importance R 2 (train) = 0.399 ± 0.054 R 2 (CV) = 0.285 ± 0.032 (a) confidence competence student teacher mathematician doctor rookie Rel. Confidence Alignm… view at source ↗
Figure 13
Figure 13. Figure 13: Results for the MMLU-Pro dataset with GPT-5.4 Mini and communication style prompts. Coefficients for a random forest regression predicting influence (a) and a random forest classifying the most influential agent in a MAS (b), with reported CV R2 and Acc respectively. The high CV score, especially on the classification task (b) suggests the defined variables are highly predictive of the FJ dynamics. 23 [P… view at source ↗
Figure 14
Figure 14. Figure 14: Results for the MMLU-Pro dataset with GPT-5.4 Mini and communication style prompts. When relating confidence and relative confidence to competence (a), we see a clear trend: confidence agents are more competent. We report Spearman’s ranked correlation per MAS. (b) An agents influence is related to its stubbornness γ. 0.00 0.25 0.50 0.75 1.00 Influence 0.0 0.2 0.4 0.6 0.8 1.0 Belief in correct answer r per… view at source ↗
Figure 15
Figure 15. Figure 15: Results for the MMLU-Pro dataset with GPT-5.4 Mini and communication style prompts. More competent agents gain more influence (a) and relative influence (b), we again report Spearman’s ranked correlation per MAS. sample 186 sample 215 sample 223 sample 151 sample 113 sample 139 sample 193 sample 266 sample 288 sample 290 Init Final 0 1 W 0 1 gamma Indicator (intensity = conf.) Correct Incorrect [PITH_FUL… view at source ↗
Figure 16
Figure 16. Figure 16: Exemplary questions of MMLU-Pro with communication style prompts with [PITH_FULL_IMAGE:figures/full_fig_p024_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Confusion matrices showing empirical result of whether per sample version of Eq. [PITH_FULL_IMAGE:figures/full_fig_p025_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Weight heatmaps for samples from the MMLU-Pro dataset with [PITH_FULL_IMAGE:figures/full_fig_p030_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: More weight heatmaps for samples from the MMLU-Pro dataset with [PITH_FULL_IMAGE:figures/full_fig_p031_19.png] view at source ↗
read the original abstract

The effectiveness of multi-agent LLM deliberation depends not only on the agents' individual predictions, but also on how they communicate and collaborate. We study this mechanism through the lens of Friedkin-Johnsen (FJ) opinion dynamics, a tractable model for analyzing stubbornness, influence, and opinion change in multi-agent systems that captures empirically observed deliberation patterns. We show that the FJ parameters are input-dependent, turning multi-agent deliberation into a mixture of experts. This perspective implies that multi-agent systems can outperform single agents and static ensembles when routing reflects agent competence. Since competence is latent in practice, we analyze how influence is established through observable proxies: agents' self-assessed confidence, their perceived confidence, and initial alignment with other agents' views.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper models multi-agent LLM deliberation using the Friedkin-Johnsen (FJ) opinion dynamics framework. It claims that the FJ parameters are input-dependent, which recasts the deliberation process as a mixture of experts. This is used to argue that multi-agent systems can outperform single agents and static ensembles when influence routing aligns with latent agent competence, with influence analyzed via observable proxies including self-assessed confidence, perceived confidence, and initial alignment.

Significance. If the central modeling assumption holds, the work supplies a tractable analytic lens for influence and routing in multi-agent LLM systems, connecting classical opinion dynamics to modern LLM collaboration and offering a route to dynamic, competence-aware ensembles.

major comments (2)
  1. [Abstract] Abstract: The claim that the FJ model 'captures empirically observed deliberation patterns' is presented without any quantitative support (parameter recovery, trajectory matching, or predictive accuracy against observed LLM opinion updates). This assumption is load-bearing for the subsequent interpretation that input-dependent parameters create a mixture-of-experts routing mechanism.
  2. [Abstract] The manuscript provides no empirical validation that the FJ model accurately reproduces deliberation dynamics in actual multi-agent LLM interactions. Without such evidence, the claims that input-dependent parameters enable performance gains over static ensembles and that competence can be proxied by the listed observables do not transfer to the target systems.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and detailed report. The two major comments both concern the empirical grounding of the Friedkin-Johnsen modeling assumption. We address each point below and will revise the manuscript to clarify the scope of our claims.

read point-by-point responses
  1. Referee: [Abstract] Abstract: The claim that the FJ model 'captures empirically observed deliberation patterns' is presented without any quantitative support (parameter recovery, trajectory matching, or predictive accuracy against observed LLM opinion updates). This assumption is load-bearing for the subsequent interpretation that input-dependent parameters create a mixture-of-experts routing mechanism.

    Authors: We agree the abstract phrasing is imprecise. The statement references the established literature on FJ dynamics in social systems rather than new quantitative validation on LLM trajectories. We will revise the abstract to read that the FJ model 'provides a tractable analytic framework previously shown to capture patterns in human deliberation' and will add an explicit caveat that direct parameter recovery or trajectory matching on LLM data is left for future work. The mixture-of-experts interpretation follows mathematically from the demonstrated input dependence and does not require the stronger empirical claim. revision: yes

  2. Referee: [Abstract] The manuscript provides no empirical validation that the FJ model accurately reproduces deliberation dynamics in actual multi-agent LLM interactions. Without such evidence, the claims that input-dependent parameters enable performance gains over static ensembles and that competence can be proxied by the listed observables do not transfer to the target systems.

    Authors: The manuscript is primarily a theoretical contribution that derives the input-dependent FJ equivalence and the resulting mixture-of-experts view, then analyzes observable influence proxies under that model. We do not present new experiments showing that FJ reproduces LLM deliberation trajectories. We will therefore (i) add a limitations paragraph stating that performance gains are conditional on the modeling assumption holding for LLMs and (ii) rephrase the relevant claims to indicate they are implications of the model rather than validated predictions. These changes will prevent over-transfer of the results to deployed systems. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation relies on external model assumption without self-referential reduction

full rationale

The provided abstract and context present the Friedkin-Johnsen model as an adopted lens that 'captures empirically observed deliberation patterns,' followed by analysis showing input-dependent parameters that reframe deliberation as a mixture of experts. No equations, parameter-fitting steps, or self-citations are quoted that reduce any claimed prediction or uniqueness result to the inputs by construction. The central modeling choice functions as an independent assumption rather than a fitted quantity renamed as output, and the paper's claims about competence proxies and performance advantages remain logically downstream of that assumption without circular collapse. This is the most common honest finding for papers that introduce an external dynamical model.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract only; no free parameters, axioms, or invented entities are specified in the provided text.

pith-pipeline@v0.9.1-grok · 5660 in / 981 out tokens · 23170 ms · 2026-06-29T19:24:25.744083+00:00 · methodology

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