Network Topology Does Not Matter: The Breakdown of Classical Consensus in LLM Populations

Sahil Rajesh Dhayalkar

cs.MAOct 24, 2026

Network Topology Does Not Matter: The Breakdown of Classical Consensus in LLM Populations

Authors: Sahil Rajesh Dhayalkar

Organizations: Arizona State University

Abstract

As multi-agent language model networks become widely deployed, predicting their collective behavior is a critical challenge. Classical distributed consensus theory relies on network topology to predict convergence, structurally assuming that agent updates are convex combinations, population means are conserved, and weights are content-independent. In this work, we demonstrate that these foundational assumptions fail for large language models (LLMs). By deterministically extracting continuous credence from token-level probabilities across eight instruction-tuned models and 73,080 controlled exchanges, we directly measure the empirical LLM update operator. We find that LLMs systematically violate convexity by updating outside the hull of observed opinions, exhibiting active repulsion (negative weights) that fundamentally breaks row-stochastic modeling and standard bounded-confidence repairs. Scaling these empirically fitted operators to simulations of 10,000 agents reveals that algebraic connectivity explains almost none of the final outcome variance. Instead, population dynamics are governed entirely by the model's internal update bias and message framing. Consequently, populations of several models, including those with up to 7B parameters, reliably compound small local drifts to reach confident agreement on objectively false claims regardless of their network structure. Our results prove that classical graph-theoretic metrics are inadequate for LLM populations, highlighting a profound deployment risk where multi-agent deliberation predictably saturates in collective delusion.

Figures & tables

Claim	Evidence	Requirement
Prop. 4.1	E1, E2	Updates escape the hull, and the population diameter consequently grows
Cor. 4.2	E1	The configuration $\lambda<0$ is reachable
Prop. 4.3	E1, E2, E3	A bias $b$ exists, and the destination ceases to track the initial condition
Cor. 4.4	E2, E3	Populations with $b>0$ on a false claim converge to belief in it
Prop. 4.5	E1, E3	$\lambda$ varies with framing, and identical graphs consequently diverge

Table 1: Mapping from formal claim to supporting evidence.

Model	Family	A1 esc.	strict	$\lambda{<}0$	A2 $\|$ drift $\|$	$\Delta$ true	$\Delta$ false
Qwen2.5-0.5B	Qwen	68.3%	38.0%	21.9%	0.252	+0.229	+0.248
Qwen2.5-1.5B	Qwen	46.9%	10.2%	18.6%	0.144	+0.100	+0.096
Qwen2.5-3B	Qwen	22.3%	8.5%	8.1%	0.069	+0.003	-0.070
Qwen2.5-7B †	Qwen	38.1%	12.7%	21.5%	0.086	+0.069	-0.025
gemma-3-4b	Gemma	34.0%	8.0%	13.2%	0.097	+0.102	-0.015
gemma-2-9b †	Gemma	38.0%	4.9%	24.2%	0.076	+0.107	-0.040

Table 2: Failure of the three assumptions across eight models; classical theory predicts zero throughout. A1 esc.: updates leaving the hull; strict: only those against the model’s no-peer drift.

\lambda<0

: updates moving away from the peer. A2

|

drift

|

: mean absolute change in the pair mean;

\Delta

true,

\Delta

false: signed drift by claim type. † Run in 4-bit.

Figure 1: Failure of all three structural assumptions across eight models. (a) The distribution of the realized weight $\lambda$ , with the shaded band indicating the only values classical theory permits. (b) The pair mean before and after a symmetric exchange, where the dashed diagonal represents what conservation requires. (c) The mean realized weight by framing, with framings ordered by message length, so that a pure verbosity effect would appear as a monotone trend.

Figure 2: Population outcomes at $n=10^{4}$ . (a) Final credence on false claims for each model. (b) True and false claims compared. Qwen2.5-3B, Llama, Mistral and Gemma-2 end below $0.5$ on false claims.

	Final mean by framing				Spread
Operator	neut.	asrt.	hedg.	verb.	mean	max
Qwen2.5-0.5B	0.946	0.777	0.958	0.953	0.181	0.304
Qwen2.5-1.5B	0.904	0.946	0.873	0.841	0.116	0.388
Qwen2.5-3B	0.445	0.299	0.607	0.495	0.431	0.851
Qwen2.5-7B	0.763	0.481	0.488	0.732	0.358	0.776
gemma-3-4b	0.811	0.484	0.532	0.709	0.346	0.659

Table 3: Final population mean under each message framing, with the graph, the density, the seed, the initial condition, and the neighbour draws held identical across framings. The per cell spread is the range across the four framings within a single sweep cell, and is therefore a matched comparison rather than a difference of averages.

Figure 3: Validation against eighty populations of twelve real Qwen2.5-3B agents. (a) Trajectories on a false claim, in which DeGroot rises toward the conserved initial mean while the real population falls. (b) One step teacher forced prediction against ground truth. (c) Prediction error by topology.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

ID	Truth	Proposition text (verbatim)
t1	true	“Water expands when it freezes.”
t2	true	“Iceland has no native mosquito population.”
t3	true	“The human genome contains fewer than 30,000 protein-coding genes.”
t4	true	“Venus rotates on its axis in the opposite direction to most planets.”
t5	true	“Octopuses have three hearts.”
t6	true	“Bananas are botanically classified as berries.”

Appendix

Table 4: The forty-five propositions, verbatim. E1 uses all forty-five. E2 and E3 use the four marked t1 , f1 , f3 , u2 .

Framing	Words	Template (verbatim)
neutral	7	Another participant said: “My estimate is {xj}%.”
assertive	15	Another participant, who seemed highly confident, said: “I’m certain about this one. It is {xj}%.”
hedged	19	Another participant, who seemed quite unsure, said: “I really don’t know, I’m just guessing here, but maybe around {xj}%.”
verbose	21	Another participant, who was also taking part in this same estimation task today, said: “My estimate for this one is {xj}%.”
control	—	No peer message is shown. See Section B.3 .

Appendix

Table 5: Message framings. All four peer framings carry an identical numeric value and differ only in wording.

Multi-Agent Consensus

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Sep 27, 2026

Collective Regimes in Multi-Agent LLMs under Reasoning Effort and Communication Topology

Multi-agent LLM systems are increasingly used for deliberation and evaluation, often under the assumption that greater peer interaction leads to more reliable consensus. Existing work largely evaluates these systems through final accuracy or aggregate agreement. However, such measures do not reveal how agreement is organized in the panel. In this paper, we study N = 50 stateless LLM agents that update their predictions from locally visible peers, and characterize their behavior using both global and local measurements of agreement. We identify three collective regimes: synchronised, twisted (locally ordered but globally incoherent) and chimera-like, where coherent and incoherent subpopulations coexist. Increasing reasoning effort in gpt-5-mini shifts panels from variable, often fragmented outcomes toward locally ordered twisted states, and a small follow-up shows such states can also form from permuted initial conditions, whereas increasing communication connectivity drives them toward global synchronisation. Fragmentation collapses faster as algebraic connectivity increases across rewired graphs. The topology effect also appears on a non-circular judging task and across models from three providers. Finally, low spatial heterogeneity does not guarantee global consensus: 40% of trials with Delta Z below 0.03 retain a twisted configuration through the final 20 turns. These results show that reasoning effort and communication topology control different aspects of multi-agent coordination, and that aggregate agreement alone is insufficient to characterize collective LLM behavior.

Machiko Hirota, Akshara Nadayanur Sathis Kanna, Ujwal Kumar +1

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Oct 14, 2026

Drivers of LLM Consensus Formation Under Competing Incentives: A Simulation Study

Large Language Models (LLMs) are increasingly deployed in multi-agent environments that produce unanimous agreement, both in intended interactions that need coordination and in unintended emergent interactions. Consequently, understanding how LLMs with competing incentives reach consensus is crucial to better interpret and design LLM collectives. We introduce an evaluation, based on the Network Consensus game, to assess the mechanisms driving this process. Here, a network of agents must agree on one of two colours to receive a payoff, but agents are offered different payoffs for the agreed colour. We vary components such as communication access and network structure and assess six open-source models and one closed model (ChatGPT 5.6-sol). We find that open-source LLMs reach consensus less often than humans in comparable experiments and only if messages are communicated across the global network. ChatGPT 5.6-sol, however, is able to reach consensus with communication limited to its neighbours and with no communication ability. This is achieved through lower stubbornness and higher majority-following tendencies, and by providing more information about its neighbours' states in messages. However, situating agents in a highly clustered graph reduces consensus, regardless of these traits, demonstrating that both system design and individual model traits drive collective outcomes.

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