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arxiv: 2606.17657 · v1 · pith:XUY6VAYXnew · submitted 2026-06-16 · 💻 cs.AI

Using Cognitive Models to Improve Language Model Simulation of Human Persuasion Games

Zirui Cheng , Zeyu Shen , Thomas L. Griffiths , Peter Henderson This is my paper

Pith reviewed 2026-06-27 01:00 UTC · model grok-4.3

classification 💻 cs.AI
keywords cognitive modelspersuasion gameslanguage model simulationreinforcement learningbelief updatingBayesian updatingmotivated reasoningdecision making
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0 comments X

The pith

Cognitive models from psychology and economics let language models simulate varied human belief updates in persuasion games.

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

Humans update beliefs differently in strategic settings, with some following Bayesian rules while others show biases such as motivated reasoning or affine distortions. Large language models used for simulation often default to narrow assumptions and miss this range. The paper tests prompting large models and reinforcement learning on small models to match specific mathematical cognitive models in legal persuasion games. Reinforcement learning reduces belief prediction error by 26.5 percent on unseen cases, and training on multiple model types raises persuasion success by 2.5 to 12 percent over Bayesian-only baselines. These varied simulations then serve as richer training environments for other models.

Core claim

Equation-to-Behavior Prompting lets large models approximate cognitive models of belief updating while Equation-to-Behavior RL trains small models to follow the same equations, cutting belief error by 26.5 percent out of distribution. Training small models on multiple decision-maker types (Bayesian, affine distortion, motivated updating, Grether's α-β) improves average belief change by 2.5-12 percent compared with Bayesian-only training, including when the target is GPT-5-mini.

What carries the argument

Equation-to-Behavior RL, which uses reinforcement learning to make small models produce outputs that match the mathematical rules of cognitive models during persuasion game turns.

If this is right

  • RL training cuts belief error by 26.5 percent for small models on out-of-distribution parameter settings.
  • Diverse cognitive-model training raises average belief change by 2.5 to 12 percent over Bayesian-only training.
  • The resulting simulations supply varied training environments that improve persuasion performance even against GPT-5-mini.
  • Small models can approximate the target cognitive models after RL training where prompting alone fails.

Where Pith is reading between the lines

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

  • The method could be tested on strategic games outside legal decision-making to check whether the same gains appear.
  • It opens a route to studying cognitive models that are mathematically defined but too intricate for direct human experiments.
  • Safety evaluations that rely on simulated humans could incorporate bias patterns that current Bayesian defaults omit.

Load-bearing premise

The four listed cognitive models and the legal decision-making persuasion games capture enough of the variety in human strategic behavior for the simulations to be useful.

What would settle it

Running the same persuasion games with real human participants as the decision-makers and checking whether belief changes match the patterns produced by the RL-trained simulations more closely than Bayesian-only simulations.

read the original abstract

People make decisions differently in strategic interactions. Some update beliefs like a Bayesian; others exhibit biases like motivated reasoning. Although creators of large language models use simulated humans for safety evaluations and training, they often fail to cover this breadth of human behavior. We argue that cognitive science and economics provide a convenient tool for doing so, making use of mathematical models of human decision-making. We propose an approach that we call Equation-to-Behavior Prompting for guiding large language models to match cognitive models, and evaluate this approach on persuasion games based on legal decision-making. We find that large models can approximate equation-based specifications -- Bayesian updating, affine distortion, motivated updating, and Grether's $\alpha$-$\beta$ model -- using prompting, but small models fail to do so. However, training small models with reinforcement learning to adhere to mathematical rules, Equation-to-Behavior RL, reduces belief error by 26.5% in out-of-distribution parameterizations. We show that these simulations can help create diverse training environments; training small models to consider different kinds of decision-makers improves average belief change by 2.5%--12% over Bayesian-only training, even when persuading GPT-5-mini. Our work could improve human simulations for training and evaluation in increasingly realistic settings, and could also enable novel research into more complicated mathematical models of human decision-making.

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 claims that cognitive models from economics and cognitive science (Bayesian updating, affine distortion, motivated updating, Grether's α-β) can be used to improve LLM-based simulations of human behavior in legal persuasion games. It introduces Equation-to-Behavior Prompting, which works for large models, and Equation-to-Behavior RL, which reduces belief error by 26.5% for small models on out-of-distribution parameterizations. It further claims that training against diverse simulators (rather than Bayesian-only) yields 2.5–12% gains in average belief change, even when the target is GPT-5-mini.

Significance. If the central modeling assumption holds, the work supplies a concrete mechanism for injecting mathematically specified heterogeneity into LLM simulators, which could strengthen training environments for safety and persuasion tasks. The RL approach for enforcing equation adherence on small models is a clear technical contribution. However, the significance remains conditional on the untested claim that fidelity to these four models produces behavior closer to actual human subjects than standard Bayesian baselines.

major comments (2)
  1. [Abstract] Abstract: the headline results (26.5% belief-error reduction; 2.5–12% gains) are reported solely with respect to the target equations themselves. No human-subject data, external validation set, or comparison to observed human belief updating is described, so the claim that the resulting simulators are “more realistic” for human persuasion games lacks an empirical anchor.
  2. [Abstract] Abstract: the persuasion-game domain is described only as “based on legal decision-making,” with no specification of the game rules, payoff structure, participant pool, or how the four cognitive models were selected or calibrated to that domain. This makes it impossible to assess whether the models capture the breadth of strategic behavior the paper aims to reproduce.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback. We respond to each major comment below, acknowledging where the manuscript requires clarification or revision.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline results (26.5% belief-error reduction; 2.5–12% gains) are reported solely with respect to the target equations themselves. No human-subject data, external validation set, or comparison to observed human belief updating is described, so the claim that the resulting simulators are “more realistic” for human persuasion games lacks an empirical anchor.

    Authors: We agree that the evaluation centers on fidelity to the target cognitive models rather than new human-subject experiments. These models (Bayesian updating, affine distortion, motivated updating, Grether's α-β) are drawn from peer-reviewed literature in economics and cognitive science that has previously validated them against human data in belief-updating and persuasion settings. Our primary contribution is a method for injecting such mathematically specified heterogeneity into LLM simulators. We will revise the abstract and discussion sections to explicitly frame the realism claim as deriving from established model validity rather than direct empirical comparison in this work, and to note the absence of new human validation as a limitation. revision: partial

  2. Referee: [Abstract] Abstract: the persuasion-game domain is described only as “based on legal decision-making,” with no specification of the game rules, payoff structure, participant pool, or how the four cognitive models were selected or calibrated to that domain. This makes it impossible to assess whether the models capture the breadth of strategic behavior the paper aims to reproduce.

    Authors: The abstract is space-constrained, but the full manuscript details the game (a two-player legal persuasion setting with asymmetric information, specific payoff matrices, and belief elicitation). The four models were selected for their documented applicability to belief revision under persuasion, as established in the cited economics and psychology literature. We will expand the abstract with a concise description of the game structure and model selection rationale to address this concern. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper's results rest on an empirical pipeline: (1) prompting or RL-training small models to match explicit target equations (Bayesian updating, affine distortion, motivated updating, Grether α-β) on training parameterizations, then (2) measuring reduced belief error on held-out OOD parameterizations of those same equations, and (3) using the resulting simulators to train persuaders and reporting average belief-change gains versus a Bayesian-only baseline when evaluated against GPT-5-mini. None of these steps reduces by construction to its own inputs; each is a standard train/test split or comparative training run whose metrics are computed against independently specified targets. No self-citations, uniqueness theorems, or ansatzes are invoked as load-bearing premises. The chain is therefore self-contained against the stated external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only; ledger reflects the domain assumptions stated in the abstract.

axioms (1)
  • domain assumption The listed cognitive models (Bayesian updating, affine distortion, motivated updating, Grether's α-β) are appropriate targets for LLM simulation of human belief updating in persuasion games.
    The entire approach rests on these models being useful stand-ins for human behavior.

pith-pipeline@v0.9.1-grok · 5774 in / 1330 out tokens · 59944 ms · 2026-06-27T01:00:48.922760+00:00 · methodology

discussion (0)

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