Contagion Networks: Evaluator Preference Propagation in Multi-Agent LLM Systems

Zewen Liu

arxiv: 2606.20493 · v2 · pith:BNPTM657new · submitted 2026-06-18 · 💻 cs.LG · cs.AI· cs.MA

Contagion Networks: Evaluator Preference Propagation in Multi-Agent LLM Systems

Zewen Liu This is my paper

Pith reviewed 2026-06-29 04:50 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.MA

keywords multi-agent LLM systemsevaluator preference propagationcontagion networksspectral radiusnetwork topologycommittee size mitigationarchitectural priors

0 comments

The pith

Preferences among LLM evaluators propagate across multi-agent networks mainly through shared architectural priors rather than explicit prompts.

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

When large language models serve as evaluators in multi-agent systems, their strategy preferences spread from one agent to others through the network. In controlled tests with three agents, this spread occurs at measurable rates between 0.157 and 0.352. A neutral-prompt control shows higher overall spread than mixed prompts, revealing that common model architecture drives most of the effect while explicit prompts actually reduce it. The amount of spread also depends on how the agents connect, remaining low in chain structures but rising in fully connected ones. Enlarging the evaluator group from one to three cuts the contagion effect by nearly 69 percent.

Core claim

The paper claims that in a 3-agent DeepSeek-chat setup with distinct preference profiles, the Cross-Agent Contagion Matrix Gamma_3 records consistent propagation with gamma values in [0.157, 0.352], yet neutral prompts produce a higher spectral radius (1.498) than mixed prompts (1.299), indicating a -63.5 percent prompt contribution. Propagation falls into regimes set by rho(Gamma_N), with chain topology suppressing spread (beta_3 = 0.0126) and fully-connected topology allowing cascades, a pattern that holds across homogeneous and cross-model pools. Committee size increase from k=1 to k=3 reduces effective contagion by 68.9 percent.

What carries the argument

The Cross-Agent Contagion Matrix Gamma_N and its spectral radius rho(Gamma_N), which quantify preference spread strength and set the regime of propagation or suppression.

If this is right

Chain topologies limit preference spread while fully-connected topologies increase it.
Larger evaluator committees reduce contagion by roughly 69 percent.
Shared model architecture produces stronger contagion than explicit preference prompts.
The same topology-dependent regime shift appears in both single-model and cross-model agent groups.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The framework could be used to design agent connection patterns that intentionally limit unwanted preference alignment.
Model selection decisions may shape collective behavior in agent groups more than individual prompt tuning.
Committee sizing as a mitigation step might scale to systems with larger numbers of agents.

Load-bearing premise

The measured differences in contagion rates are caused by preference propagation rather than other uncontrolled factors in the 3-agent DeepSeek-chat setup or the specific prompt profiles chosen.

What would settle it

Repeating the neutral-prompt versus mixed-prompt comparison using agents built on unrelated model architectures and checking whether the difference in spectral radius values disappears or reverses.

Figures

Figures reproduced from arXiv: 2606.20493 by Zewen Liu.

**Figure 1.** Figure 1: Cross-agent contagion network Γ3 (mean over n = 2 seeds). All edges are dashed (γ < 1.0) indicating the suppression regime for the chain topology. The spectral radius ρ¯(Γ3) = 1.402 ± 0.003 applies to the fully-connected topology; under chain propagation, all link-level coefficients remain below 1.0, satisfying Corollary 1. 5.1 Phase 1: Baseline Preference Profiles [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗

**Figure 1.** Figure 1: Cross-agent contagion network Γ3 (representative seed; ρ = 1.391 ± 0.022, 95% CI [1.370, 1.412], n = 4 seeds). All edges are below 1.0 (dashed), placing the system in the suppression regime under chain topology. The spectral radius ρ(Γ3) exceeds 1.0 for all 4 seeds—the same agents that suppress preference contagion in chain configuration would enter cascade in a fully-connected network, a theoretical pred… view at source ↗

**Figure 2.** Figure 2: Per-hop contagion coefficients along the 3-agent chain. All hops are below the cascade [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 2.** Figure 2: Convergence analysis justifying R = 20 rounds. (a) Strategy weights converge within 10–15 rounds for γ = 0.2. (b) Gamma proxy (rate of strategy similarity change) converges for different γ values. (c) Convergence round vs. γ: for γ < 0.35, convergence occurs within 20 rounds. (d) Measured gamma proxy stabilizes after R = 15, confirming R = 20 is in the stable measurement region [PITH_FULL_IMAGE:figures/fu… view at source ↗

**Figure 3.** Figure 3: Diversity-induced reduction of effective contagion. Left: [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

**Figure 3.** Figure 3: Per-hop contagion coefficients along the 3-agent chain (original seed). All hops are [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗

**Figure 4.** Figure 4: Diversity-induced reduction of effective contagion (original seed). Left: [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗

**Figure 5.** Figure 5: Cross-model vs. homogeneous-model comparison. (a) Cross-model contagion matrix [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗

**Figure 6.** Figure 6: Nonlinear TTRL dynamics beyond the linear approximation. Top row: maximum [PITH_FULL_IMAGE:figures/full_fig_p023_6.png] view at source ↗

**Figure 7.** Figure 7: TTRL weight clipping ablation across three regimes. Left column: strategy concentra [PITH_FULL_IMAGE:figures/full_fig_p027_7.png] view at source ↗

**Figure 8.** Figure 8: TTRL learning rate sensitivity analysis. (a) Heatmap of [PITH_FULL_IMAGE:figures/full_fig_p032_8.png] view at source ↗

read the original abstract

When large language models serve as evaluators in multi-agent systems, their strategy preferences -- whether induced by explicit prompts or by shared architectural priors -- propagate through the agent network. We introduce Contagion Networks, a formal framework for measuring how evaluator preferences spread across interacting LLM agents. In a controlled 3-agent experiment using DeepSeek-chat with three distinct evaluator preference profiles (structured, balanced, evidence-based), we measure the Cross-Agent Contagion Matrix Gamma_3 and find that preferences consistently propagate between agents (gamma in [0.157, 0.352]). A neutral-prompt control experiment reveals a counter-intuitive result: shared architectural priors dominate explicit preference prompts as the driver of contagion (rho_neutral = 1.498 vs. rho_mixed = 1.299; prompt contribution: -63.5%). We identify three propagation regimes governed by the spectral radius rho(Gamma_N) and demonstrate that the same agents suppress preference contagion in chain topology (beta_3 = 0.0126 +/- 0.0038, 95% CI [0.0089, 0.0163], n=4 seeds) but cascade in fully-connected topology (Delta H_avg = -0.020) -- a topology-dependent regime transition validated both for homogeneous and cross-model agent pools (rho^cross = 1.296 +/- 0.016, n=4). We show that increasing evaluator committee size from k=1 to k=3 reduces effective contagion by 68.9% +/- 14.1% (n=4 seeds), providing an actionable mitigation strategy. We release the open-source Contagion Network experimental framework.

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.

Desk Editor's Note private letter to a colleague

The paper measures preference spread in a 3-agent LLM setup and reports that model priors outweigh prompts while topology and committee size modulate it, but the abstract leaves the actual interaction mechanism unverified.

read the letter

The main takeaway is that this work defines a contagion matrix for LLM evaluators and reports concrete numbers: gamma between 0.157 and 0.352, spectral radius higher under neutral prompts than mixed ones, chain topology suppressing spread while fully connected increases it, and committee size cutting effective contagion by roughly 69 percent. They also release the experimental code.

What stands out is the attempt to separate architectural priors from explicit prompts via the neutral control and the topology comparison across both same-model and cross-model pools. Reporting intervals and seed counts is better than many LLM papers. The regime classification via spectral radius is a straightforward application of linear algebra to the measured matrix.

The weak point is that the central claim of interaction-driven propagation still rests on the assumption that agents are actually conditioning on each other's outputs in a way that transmits preferences. The abstract describes fixed profiles and a neutral-prompt baseline, but gives no detail on message format, temperature, or verification that one agent's output reaches the next. In a setup using identical DeepSeek-chat instances, correlated behavior from shared priors remains a plausible alternative to the reported contagion effects. The stress-test concern lands here.

This is for researchers already running multi-agent evaluator committees who need a way to quantify and reduce preference bleed. It is worth sending to referees because the framework and the quantitative mitigation claim are specific enough to test, even if the current write-up is thin on methods.

Referee Report

2 major / 2 minor

Summary. The paper introduces Contagion Networks as a framework for measuring how evaluator preferences propagate across interacting LLM agents. In a controlled 3-agent experiment with DeepSeek-chat using structured, balanced, and evidence-based profiles, it reports a Cross-Agent Contagion Matrix Gamma_3 with gamma values in [0.157, 0.352], finds shared architectural priors dominate explicit prompts (rho_neutral = 1.498 vs. rho_mixed = 1.299; prompt contribution -63.5%), identifies three regimes governed by the spectral radius rho(Gamma_N), shows topology-dependent effects (chain suppresses with beta_3 = 0.0126 +/- 0.0038 while fully-connected cascades with Delta H_avg = -0.020), and reports that increasing committee size from k=1 to k=3 reduces contagion by 68.9% +/- 14.1% (n=4 seeds). The open-source framework is released.

Significance. If the causal attribution to interaction-driven propagation holds, the work offers a quantitative approach to preference dynamics in multi-agent LLM evaluators, with actionable findings on topology and committee size as mitigations. The reproducible code release and use of confidence intervals with seed counts are strengths that support verification. The counter-intuitive dominance of model priors over prompts could influence preference engineering practices. Results are currently limited to DeepSeek-chat and the chosen profiles, so broader impact depends on validation in other settings.

major comments (2)

[Abstract (controlled 3-agent experiment and neutral-prompt control)] Abstract (controlled 3-agent experiment and neutral-prompt control description): The central claim that gamma values, rho_neutral vs. rho_mixed differences, and topology effects are caused by preference propagation requires explicit documentation of the interaction protocol (message content passed between agents, temperature settings, and verification that agents condition on each others' outputs). Without these, shared model priors or prompt artifacts remain a plausible alternative for the measured Gamma_3 matrix and regime shifts, as the neutral-prompt control alone does not isolate interaction effects in the fixed DeepSeek-chat setup.
[Propagation regimes (governed by spectral radius rho(Gamma_N))] Propagation regimes section (governed by spectral radius rho(Gamma_N)): The manuscript identifies three regimes based on rho(Gamma_N) and validates the topology-dependent transition for both homogeneous and cross-model pools (rho^cross = 1.296 +/- 0.016), but does not provide the explicit thresholds, derivation, or independent test linking the spectral radius to the observed beta_3 suppression or Delta H_avg cascade. This leaves the regime claims dependent on the specific experimental measurements rather than a general property of the matrix.

minor comments (2)

[Abstract] The abstract reports quantitative results with 95% CIs and n=4 seeds but provides no pointer to the methods, equations for Gamma_3, or raw data; adding a brief methods reference would improve clarity.
[Introduction/Methods] Notation for new entities (Contagion Networks, Gamma_3, beta_3) is introduced without a dedicated preliminary definitions subsection, which could be clarified for readers unfamiliar with the framework.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and valuable feedback on our manuscript. We address each major comment point by point below, providing clarifications and committing to revisions where they strengthen the paper without misrepresenting the existing experiments.

read point-by-point responses

Referee: [Abstract (controlled 3-agent experiment and neutral-prompt control)] Abstract (controlled 3-agent experiment and neutral-prompt control description): The central claim that gamma values, rho_neutral vs. rho_mixed differences, and topology effects are caused by preference propagation requires explicit documentation of the interaction protocol (message content passed between agents, temperature settings, and verification that agents condition on each others' outputs). Without these, shared model priors or prompt artifacts remain a plausible alternative for the measured Gamma_3 matrix and regime shifts, as the neutral-prompt control alone does not isolate interaction effects in the fixed DeepSeek-chat setup.

Authors: We agree that explicit documentation of the interaction protocol is necessary to fully support the causal interpretation. The neutral-prompt control compares contagion under mixed vs. neutral prompts within the same interacting setup, which isolates the incremental effect of explicit prompts beyond architectural priors; however, we acknowledge that without detailed protocol description this isolation may not be immediately clear to readers. In the revised manuscript we will add a dedicated 'Interaction Protocol' subsection in the Methods that specifies: (i) the exact message content and format passed between agents, (ii) temperature and other generation parameters, and (iii) verification steps confirming agents condition on prior outputs. This will allow readers to assess whether shared priors or artifacts remain plausible alternatives. revision: yes
Referee: [Propagation regimes (governed by spectral radius rho(Gamma_N))] Propagation regimes section (governed by spectral radius rho(Gamma_N)): The manuscript identifies three regimes based on rho(Gamma_N) and validates the topology-dependent transition for both homogeneous and cross-model pools (rho^cross = 1.296 +/- 0.016), but does not provide the explicit thresholds, derivation, or independent test linking the spectral radius to the observed beta_3 suppression or Delta H_avg cascade. This leaves the regime claims dependent on the specific experimental measurements rather than a general property of the matrix.

Authors: The regimes are motivated by standard results from linear dynamical systems, where the spectral radius rho(Gamma_N) determines stability: rho < 1 implies asymptotic decay of preference deviations, rho = 1 implies marginal persistence, and rho > 1 implies amplification. We will add explicit numerical thresholds together with a short derivation from the matrix iteration x_{t+1} = Gamma_N x_t in the revised Propagation regimes section. The topology-dependent transitions (chain suppression vs. fully-connected cascade) are demonstrated empirically for both homogeneous and cross-model pools, providing evidence that the spectral-radius prediction holds beyond a single measurement set. While a fully independent theoretical simulation (e.g., on synthetic matrices) is not present in the current draft, the cross-model validation already moves the claim beyond purely experiment-specific observations; we will clarify this distinction in the revision. revision: partial

Circularity Check

0 steps flagged

No circularity; all central quantities are direct experimental measurements

full rationale

The paper defines Contagion Networks as a measurement framework and reports empirical values (Gamma_3 matrix entries, rho_neutral vs rho_mixed, beta_3, Delta H, committee-size reduction) obtained from controlled LLM agent runs. No equations derive predictions from fitted parameters, no self-citations supply load-bearing uniqueness theorems, and spectral radius is applied as standard linear algebra to the observed matrix. The derivation chain consists of data collection and standard post-processing with no reduction to inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 2 invented entities

The central claims rest on the assumption that the experimental measurements with DeepSeek-chat capture genuine preference propagation driven by the stated factors; no free parameters are explicitly fitted in the abstract, but the three preference profiles and the choice of topologies are experimental design choices.

axioms (2)

domain assumption Evaluator preferences can be reliably induced and distinguished by the three prompt profiles (structured, balanced, evidence-based) in the DeepSeek-chat model.
Invoked in the controlled 3-agent experiment description.
domain assumption The Cross-Agent Contagion Matrix Gamma_N and its spectral radius rho(Gamma_N) correctly quantify preference propagation across agent interactions.
Central to identifying the three propagation regimes.

invented entities (2)

Contagion Networks no independent evidence
purpose: Formal framework for measuring how evaluator preferences spread across interacting LLM agents
Newly introduced in the paper; no independent evidence provided outside this work.
Cross-Agent Contagion Matrix Gamma_3 no independent evidence
purpose: Matrix used to measure preference propagation between three agents
Defined and measured within the 3-agent experiment; no external validation cited.

pith-pipeline@v0.9.1-grok · 5835 in / 1531 out tokens · 28282 ms · 2026-06-29T04:50:37.922439+00:00 · methodology

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Forward citations

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Reference graph

Works this paper leans on

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2024

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L. Pan, A. Korthikanti, M. Brahmbhatt, et al.Improving Code Generation by Training with Human Feedback on Execution.arXiv:2303.05330, 2023. A Proof of Propagation Regime Theorem Proof.Letw (t) ∈R N be the vector of strategy concentration indices (e.g.,maxk w(t) ik , the max- imum strategy weight for each agent) at iterationt. In the linear regime near the...

Pith/arXiv arXiv 2023

[25] [25]

In the suppression regime (ρ(ΓN)≈1), all off-diagonal terms are small relative to the self- influence term (γij ≪1), and the dominant eigenvalue is dominated by the unit diagonal

[26] [26]

A" or "B

In the cascade regime (ρ(ΓN)>1), the off-diagonal structure creates a cyclic feedback path (e.g.,A→B→C→A) with net gain>1, which is captured by the spectral radius exceeding the baseline of 1. The key insight:ρ(Γ N)−1measures the excess growth contributed by network structure alone. This is mathematically valid regardless of whether the full state transit...