Coherence-Driven Belief Formation and Population Dynamics of Contagion in LLM Agents

Tathagata Banerjee; Nima Moghaddas

cs.AIOct 2, 2026

Coherence-Driven Belief Formation and Population Dynamics of Contagion in LLM Agents

Authors: Tathagata Banerjee, Nima Moghaddas

Organizations: Northeastern University

Abstract

Models of social contagion usually assume how individuals adopt beliefs and derive population behavior from it. We instead empirically measure belief adoption in language model agents, quantifying the probability an agent adopts a claim given how many peers endorse it. We find this adoption kernel to be sigmoid, a characteristic of complex contagion, with a threshold that is sensitive to three sources: the claim's plausibility, the source's reliability, and the agent's disposition. These three dimensions are well approximated by a single effective dimension which we propose can be understood as the coherence of the incoming belief with the LLM agent's prior beliefs. Further, we observe a characteristic of complex contagion in the collective dynamics of belief adoption in a system of AI agents: further spread on clustered than random networks. These systems also exhibit a bifurcating cascade window, and self-sustaining hysteretic consensus which lead to consensus being far harder to remove than to establish.

Figures & tables

Figure 1: Belief adoption is coherence-driven and reduces to one effective dimension. (a) Adoption kernels $p_{\mathrm{adopt}}(k)$ for plausible / borderline / implausible claims; less plausible claims require more endorsing peers, raising the threshold. (b) Adoption threshold across claim plausibility and source reliability: expert sources lower the threshold and compensate for implausibility, while an unreliable source raises it. (c, d) Kernels for four personas at two plausibility levels, tracing the resilience ladder from hardened (ignores peers) through trusting to credulous (adopts at minimal pressure). (e-g) The three axes are modifiable coherence relations: installing (e) a world prior, (f) a source-reliability belief, or (g) a coherence-weighting instruction moves the threshold in the direction a coherence account predicts. (h) Kernels shifted by their own threshold collapse onto a single master curve (individual conditions in colour, mean in black), and (i) an additive model predicts the threshold across the $3{\times}3{\times}3$ grid. The threshold tensor is one-dimensional (first PC 98% ) and additive ( 92% ).

Figure 2: Population dynamics of the measured kernel. (a) Ignition probability and mean final cascade size vs. claim plausibilit; the cascade window closes through a saddle-node-like transition as plausibility falls. (b) Per-condition final belief fraction: outcomes are monostable on either side of the transition and bimodal within it. (c) Complex contagion: at matched degree, clustered networks (ring,

C{=}0.60

) produce larger cascades than random networks (

C{=}0.20

), points are individual runs, black shows the mean with

95\%

bootstrap CI (d-f) Hysteresis for plausible, borderline, and implausible claims: Consensus is self-sustaining; the down-path stays locked at full adoption and the loop (shaded) widens with implausibility.

	Qwen / temp.	Mistral / temp.	Qwen / traffic
Reduction: 1st PC (%)	98	96	97
Reduction: additivity $R^{2}$ (%)	92	80	91
Clustering: $p$ (MW $U$ )	2.7e-6	4.1e-3	7.1e-3
Clustering: effect	+0.37	+0.21	+0.20
Hysteresis loop (plaus.)	0.067	0.000	0.065
Hysteresis loop (implaus.)	0.252	0.248	0.248

Table 1: Central quantities across the primary condition and two robustness axes. The reduction (dimensionality), the clustering contrast, and the hysteresis loop ordering reproduce in every condition.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Figure A.1 : Mistral: Belief adoption is coherence-driven and reduces to one effective dimension. (a) Adoption kernels for plausible / borderline / implausible claims; the threshold rises with implausibility. (b) Adoption threshold across claim plausibility and source reliability; expert sources lower the threshold, but an unreliable source pins it at the ceiling for every claim, a more categorical source axis than Qwen. (c) Kernels per persona at a fixed plausibility level and (d) the same under a stronger claim, tracing the resilience ladder from hardened (never adopts) to credulous. (e-g) The three axes as editable coherence relations: installing (e) a world prior (temperature), (f) a source-reliability belief, and (g) a coherence-weighting instruction each moves the threshold in the coherence-predicted direction. (h) Kernels shifted by their own threshold collapse onto one master curve (individual conditions in colour, mean in black). (i) Additive prediction vs. observed threshold across the $3{\times}3{\times}3$ grid. The threshold tensor is one-dimensional (first PC 96% ) and additive ( 80% )

Figure A.2 : Population dynamics of the measured kernel. (a) Ignition probability and mean final cascade size vs. claim plausibilit; the window closes through a sharp bifurcation. (b) Per-condition final belief fraction, monostable on either side and bimodal within the narrow transition zone. (c) Complex contagion: at matched degree, clustered (ring,

C{=}0.60

) networks produce larger cascades than random (

C{=}0.20

) networks (points are individual runs; black shows mean with

95\%

bootstrap CI) (d-f) Hysteresis for plausible, borderline, and implausible claims. Consensus is self-sustaining and the loop (shaded) widens with implausibility.

Figure B.1 : Traffic domain, Belief adoption is coherence-driven and reduces to one effective dimension. (a) Adoption kernels for plausible (35 min) / borderline (3 h) / implausible (6 h) commute-time claims; the threshold rises with implausibility. (b) Adoption threshold across claim plausibility and source reliability; expert sources lower the threshold while an unreliable source pins it near the ceiling, reproducing the plausibility wall. (c) Kernels per persona at a fixed plausibility level and (d) the same under a stronger claim, tracing the resilience ladder from hardened (never adopts) to credulous. (e-g) The three axes as editable coherence relations: installing (e) a road-condition prior (clear / normal / gridlock), (f) a source-reliability belief, and (g) a coherence-weighting instruction each moves the threshold as a coherence account predicts; the road-condition prior acts bidirectionally , lowering the threshold for long commutes and raising it for short ones. (h) Kernels shifted by their own threshold collapse onto one master curve (individual conditions in colour, mean in black). (i) Additive prediction vs. observed threshold across the $3{\times}3{\times}3$ grid. The threshold tensor is one-dimensional (first PC 97% ) and additive ( 91% ), closely matching the temperature primary.

Figure B.2 : Population dynamics of the measured kernel. (a) Ignition probability and mean final cascade size vs. claimed commute time; the cascade window closes through a clean transition at a commute of

\sim

4 hours. (b) Per-condition final belief fraction, monostable on either side and bimodal within the transition zone. (c) Complex contagion: at matched degree, clustered (ring,

C{=}0.60

) networks produce larger cascades than random (

C{=}0.20

) networks (points are individual runs; black shows mean with

95\%

bootstrap CI) (d-f) Hysteresis for plausible, borderline, and implausible claims. Consensus is self-sustaining; the down-path stays locked at full adoption and the loop (shaded) widens with implausibility, with loop areas nearly identical to the temperature primary.

Model	Decision	Token	ID
Qwen2.5-3B-Instruct	ADOPT	ADO	28814
	DECLINE	DECL	21817
	MAINTAIN	MA	4835
	ABANDON	AB	1867
Mistral-7B-Instruct-v0.3	ADOPT	AD	10772
	DECLINE	DE	5330

Appendix

Table 2: First sub-word token identifiers per model.

plausibility level	Temperature (Boston)	Traffic (I-93 commute)
plausible	22 ∘ C	35 min
borderline	35 ∘ C	3 hours
implausible	45 ∘ C	6 hours
impossible	75 ∘ C	24 hours

Appendix

Table 3: Claim values by plausibility level and domain.

Parameter	Bifurcation (§ 5.1 )	Clustering (§ 5.2 )	Hysteresis (§ 5.3 )
Network size $N$	30	30	30
Peer discretization $n$	10	10	10
Topology	scale-free (BA, $m{=}3$ )	Watts–Strogatz (deg. 6)	scale-free (BA, $m{=}3$ )
Seed fraction $\rho_{0}$	0.15	0.12	—
Rewiring $p$	—	$\{0\ (\text{ring}),\,1\ (\text{random})\}$	—
Horizon (steps)	15	15	20

Appendix

Table 4: Population simulation parameters, per experiment. Each quantity is fixed (not a range); stochasticity across replicates comes only from the random seed, enumerated

0,\dots,R-1

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Large language models (LLMs) are increasingly deployed in multi-agent environments. However, the processes by which beliefs form and propagate among interacting LLMs remain poorly understood. We introduce CoevolveSim, a framework for studying belief diffusion within networked LLM populations. CoevolveSim allows us to isolate and study three factors: domain specialization, social-role assignment, and social network structure. Within this framework, generalist and specialist LLM agents exchange and revise beliefs. In each round, an LLM agent observes a summary of its neighbors' beliefs before updating its own. We find that persona-style role assignment reshapes individual belief revision but has little effect on population-level consensus. In contrast, introducing finetuned specialist LLMs produces a large change in consensus and is accompanied by persistent asymmetries in outgoing influence. We further show that an opinion-dynamics surrogate combining individual persistence with population-level belief composition reproduces consensus with high fidelity in every scenario, whereas predicting individual final-round beliefs in heterogeneous LLM populations additionally benefits from agent identity.

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