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arxiv: 2506.17788 · v2 · submitted 2025-06-21 · 💻 cs.AI · cs.CL· cs.LG· cs.MA

Bayesian Social Deduction with Graph-Informed Language Models

Shahab Rahimirad , Guven Gergerli , Lucia Romero , Angela Qian , Matthew Lyle Olson , Simon Stepputtis , Joseph Campbell This is my paper

Pith reviewed 2026-05-19 07:24 UTC · model grok-4.3

classification 💻 cs.AI cs.CLcs.LGcs.MA
keywords social reasoninglanguage agentsprobabilistic modelsgraph structuresAvalonbelief inferencehybrid AI systems
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The pith

Externalizing belief inference to a graph-informed probabilistic model lets smaller language agents match large models and defeat humans in Avalon.

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

Social reasoning requires inferring hidden beliefs and intentions from limited observations, a task where even large language models struggle without heavy computation. This paper shows that splitting the work—using a structured graph-based probabilistic model for belief tracking and an LLM only for language—lets compact agents perform at the level of much larger systems. In tests on the social deduction game Avalon, the hybrid approach matches big models in agent play and beats human players with a 67 percent win rate while earning better ratings than human teammates. The result suggests that explicit external models for unobservables can overcome internal reasoning limits in LLMs.

Core claim

The authors demonstrate that a hybrid system, in which a graph-informed structured probabilistic model handles externalized belief inference about other players' hidden states while the language model manages only language understanding and communication, achieves competitive results against much larger pure language models in agent-versus-agent Avalon and secures a 67 percent win rate against human opponents in controlled experiments.

What carries the argument

The hybrid reasoning framework that externalizes belief inference to a graph-informed probabilistic model for tracking unobservable player intentions and beliefs.

If this is right

  • Agents can operate in real time without needing extensive test-time inference.
  • Performance holds across different model sizes when the belief model is kept separate.
  • Qualitative ratings from humans favor the hybrid agent over both reasoning baselines and fellow humans.

Where Pith is reading between the lines

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

  • The approach may extend to other domains requiring theory-of-mind reasoning, such as negotiation or collaborative planning.
  • Success against humans points to uses in social simulation and AI training environments.

Load-bearing premise

The graph-informed probabilistic model correctly extracts and represents the crucial unobservable beliefs and intentions of other agents from partial game observations.

What would settle it

A replication study in which the hybrid agent plays against humans and fails to exceed a 50 percent win rate, or in which swapping the graph model for pure LLM-based belief inference restores the performance gap seen in distilled models.

Figures

Figures reproduced from arXiv: 2506.17788 by Angela Qian, Guven Gergerli, Joseph Campbell, Lucia Romero, Matthew Lyle Olson, Shahab Rahimirad, Simon Stepputtis.

Figure 1
Figure 1. Figure 1: Overview of GRAIL’s architecture and inter [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: F1 scores of agents’ voting predictions of team composition per round (error bars indicate [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Probability density of GRAIL beliefs about Good and Evil players, with and without [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Average per-round token usage for GRAIL, LRM-based reasoning agents, and ReCon in Agent-Agent games. Belief Distribution: To analyze the effect of lan￾guage priors, we visualize the evolution of GRAIL’s belief over the course of 13 games that end in 5 rounds. Fig. 3a shows the kernel density estimations KDE(b t j | rj = 1) (Evil player) and KDE(b t j | rj = 0) (Good player), computed both with and without … view at source ↗
Figure 5
Figure 5. Figure 5: Combined ablation results across agent components, model size, and reasoning types. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Hallucination rates for GRAIL (Llama 3.1) and the rea￾soning agent (DS-R1) for different model sizes over 40 games. During experiments, we observed that agent messages some￾times included hallucinations and references to non-existent game events. To evaluate how well agents align their messages with the ground truth game state, we analyze hallucination rates in both GRAIL and the reasoning agent across var… view at source ↗
Figure 7
Figure 7. Figure 7: Average scores given to agents by humans across two questions assessing contri￾bution and helpfulness. Human ratings (Evil players’ votes for Good human players) are included for baseline comparison. H1, H2: Across 15 games, GRAIL won 10 and lost 5 (67% win rate), whereas the reasoning-based agent won 4 and lost 11 (27% win rate). To assess the statis￾tical significance of this performance difference, we e… view at source ↗
Figure 8
Figure 8. Figure 8: The Factor Graph Structure 17 [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The relationship between accuracy and confidence of the model before and after calibration. [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The game interface as seen in Spectator Mode [PITH_FULL_IMAGE:figures/full_fig_p031_10.png] view at source ↗
read the original abstract

Social reasoning - inferring unobservable beliefs and intentions from partial observations of other agents - remains a challenging task for large language models (LLMs). We evaluate the limits of current reasoning language models in the social deduction game Avalon and find that while the largest models demonstrate strong performance, they require extensive test-time inference and degrade sharply when distilled to smaller, real-time-capable variants. To address this, we introduce a hybrid reasoning framework that externalizes belief inference to a structured probabilistic model, while using an LLM for language understanding and interaction. Our approach achieves competitive performance with much larger models in Agent-Agent play and, notably, is the first language agent to defeat human players in a controlled study - achieving a 67% win rate and receiving higher qualitative ratings than both reasoning baselines and human teammates. We release code, models, and a dataset to support future work on social reasoning in LLM agents, which can be found at https://camp-lab-purdue.github.io/bayesian-social-deduction/

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 / 2 minor

Summary. The paper introduces a hybrid reasoning framework for the social deduction game Avalon that externalizes belief inference about hidden roles, intentions, and knowledge to a graph-informed structured probabilistic model while delegating language understanding and interaction to an LLM. It reports competitive performance against much larger models in agent-agent play and, in a controlled human study, a 67% win rate for the hybrid agent along with higher qualitative ratings than both reasoning baselines and human teammates. The authors release code, models, and a dataset.

Significance. If the results are robust, the work provides evidence that hybrid systems can achieve strong social reasoning with smaller, real-time LLMs by offloading complex belief tracking to an external probabilistic structure, addressing a known limitation of pure end-to-end LLM reasoning. The human-study result would constitute a notable first for language agents if the controls and statistical reporting hold. Open release of artifacts is a clear strength that supports reproducibility and follow-on research.

major comments (2)
  1. [§3] §3 (Model): The description of the graph-informed probabilistic belief model lacks explicit equations for the update rules and the representation of higher-order beliefs (e.g., nested beliefs about other agents' beliefs). Without these, it is impossible to verify whether the structure captures the deceptive or nested intentions that arise in human play, which is the load-bearing assumption for the 67% win-rate claim.
  2. [§4.3] §4.3 (Human Study): The results section reports a 67% win rate and higher qualitative ratings but provides no details on participant count, experience matching, statistical tests, or exclusion criteria. This omission prevents assessment of whether the hybrid split introduces new failure modes precisely in the human regime where superiority is claimed.
minor comments (2)
  1. [Abstract] The abstract and introduction use the term 'parameter-free' for the probabilistic component; clarify whether any hyperparameters in the graph construction or prior specification are tuned on the evaluation data.
  2. [Figure 2] Figure 2 (architecture diagram) would benefit from an explicit legend distinguishing LLM-generated text from probabilistic belief outputs to improve readability for readers unfamiliar with hybrid agent designs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our work. We provide point-by-point responses to the major comments below. We agree that additional mathematical detail and experimental reporting are needed to strengthen the manuscript and will revise accordingly.

read point-by-point responses

  1. Referee: [§3] §3 (Model): The description of the graph-informed probabilistic belief model lacks explicit equations for the update rules and the representation of higher-order beliefs (e.g., nested beliefs about other agents' beliefs). Without these, it is impossible to verify whether the structure captures the deceptive or nested intentions that arise in human play, which is the load-bearing assumption for the 67% win-rate claim.

    Authors: We acknowledge that the model section provides a high-level description of the graph-informed probabilistic belief model without explicit equations. This is a valid point, as the update rules for beliefs and the mechanism for representing higher-order beliefs are crucial for understanding how the model handles deception and nested intentions in Avalon. In the revised manuscript, we will add the formal equations for the belief update process, including how the graph structure encodes and propagates higher-order beliefs. This revision will make it possible to verify the model's capacity to support the reported performance. revision: yes

  2. Referee: [§4.3] §4.3 (Human Study): The results section reports a 67% win rate and higher qualitative ratings but provides no details on participant count, experience matching, statistical tests, or exclusion criteria. This omission prevents assessment of whether the hybrid split introduces new failure modes precisely in the human regime where superiority is claimed.

    Authors: We appreciate the referee drawing attention to the reporting standards for the human study. While the manuscript states the 67% win rate and qualitative ratings, we agree that more details are necessary for full evaluation. We will revise the section to include the number of participants, how they were matched for experience, the statistical tests conducted (including p-values), and the exclusion criteria used. These additions will allow for a better assessment of the results and any potential failure modes in human interactions. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the hybrid model or performance claims

full rationale

The paper describes a hybrid framework that externalizes belief inference to an independent structured probabilistic model over a graph of agents/roles/observations, while delegating language tasks to the LLM. No equations, derivations, or self-citations are shown that reduce the claimed win rates or competitive performance to a fitted parameter defined by the result itself, a self-referential definition, or a load-bearing uniqueness theorem from prior author work. The results are presented as empirical outcomes from agent-agent and controlled human-play experiments, with the probabilistic component described as external and structured rather than fitted to the target metrics, making the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the hybrid framework implicitly relies on standard Bayesian updating assumptions and LLM language capabilities, but none are detailed enough to enumerate.

pith-pipeline@v0.9.0 · 5724 in / 1265 out tokens · 27477 ms · 2026-05-19T07:24:16.591106+00:00 · methodology

discussion (0)

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Forward citations

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