MarPT

📄 arXiv

This is the official repository for the paper "Rethinking Prospect Theory for LLMs: Revealing the Instability of Decision-Making under Epistemic Uncertainty".

🎯 Project Overview

MarPT investigates whether Prospect Theory (PT) — a classic framework for modeling human decision-making under uncertainty — adequately describes the decision-making behavior of Large Language Models (LLMs), and whether PT parameter estimates remain stable when numerical probabilities are replaced by linguistic uncertainty (epistemic markers such as "likely" or "highly unlikely").

Grounded in a classic behavioral economics experimental paradigm, the repository provides:

• 📏 PT Parameter Estimation: Estimates PT parameters (σ, λ, γ) of LLMs from economics-style binary-choice questions via maximum likelihood estimation
• 📊 Fitness Evaluation: Evaluates how well the fitted PT model captures LLM decision-making with MAE and McFadden R²
• 🗣️ Marker Mapping: Derives probability mappings for 14 epistemic markers (from "almost certain" to "highly unlikely") in the same decision context
• 🔄 Stability Re-measurement: Injects the derived marker mappings back into the prompts and re-measures PT parameters to test robustness under linguistic uncertainty

Our findings suggest that PT does not consistently provide a reliable account of LLM decision-making across models, and that its application to LLMs is likely not robust to epistemic uncertainty — cautioning against the deployment of PT-based frameworks in real-world applications where epistemic ambiguity is prevalent.

Figure 1: Overview of the three-stage workflow. (1) Decision-Making Behavior Evaluation: the model answers a series of binary-choice economics questions to estimate baseline PT parameters. (2) Markers Mapping: probability mappings for epistemic markers are derived from switching points between options with numerical and linguistic probabilities. (3) Add with Uncertainty: numerical probabilities are substituted with epistemic markers and PT parameters are re-measured to test stability.

✨ Core Features

• 🧪 Classic Experimental Paradigm: A streamlined three-stage workflow adapted from behavioral economics (Tversky & Kahneman style lottery-choice tasks)
• 🤖 Multi-Model Support: Evaluated on Llama-3.1-8B-Instruct, Mistral-7B-Instruct-v0.3, and Qwen2.5-7B/14B/32B-Instruct
• 🔌 Unified Generation Module: A shared VLLMGenerator client that talks to any vLLM-served model via the OpenAI-compatible API
• 📈 MLE-based Estimation: PT parameters fitted via maximum likelihood estimation with bootstrap confidence intervals
• 📝 14 Epistemic Markers: Systematic probability mappings for a full spectrum of linguistic uncertainty expressions
• 🧩 Modular Design: Each experimental stage is a self-contained directory with its own elicitation, processing, and analysis scripts

📁 Directory Structure

MarPT/
├── figures/                # Paper figures
├── generator/              # Unified LLM generation module
│   ├── client.py           # VLLMGenerator (OpenAI-compatible API client)
│   └── .sh/                # Server / batch scripts
├── risk/                   # Stage 1: baseline PT parameter estimation
├── marker/                 # Stage 2: probability mapping of epistemic markers
├── risk_marker/            # Stage 3: PT re-measurement with marker substitution
└── requirements.txt

Each stage directory is self-contained:

risk/ (and marker/, risk_marker/)
    |---plot/               # Visualization outputs
    |---processed/          # Measured parameters and processed results
    |---result/             # Raw elicitation outputs
    analyze.py              # Analysis and plotting
    elicitation.py          # Main experiment entry point
    mle.py                  # MLE fitting of PT parameters
    process.py              # Result processing
    prompt.py               # Prompt construction

🔄 Workflow

1. Stage 1 — Baseline PT Estimation (risk/)
   Binary-choice questions with numerical probabilities
   └── MLE fitting → baseline PT parameters (σ, λ, γ) + fitness metrics

2. Stage 2 — Marker Mapping (marker/)
   Switching-point elicitation between numerical and linguistic probabilities
   └── Probability mapping for each epistemic marker (e.g., "highly unlikely" → 10%)

3. Stage 3 — Re-measurement under Uncertainty (risk_marker/)
   Numerical probabilities replaced by epistemic markers
   └── Re-estimated PT parameters → stability comparison against baseline

📊 Key Results

Figure 2: Derived probability mappings (switching probability) for 14 epistemic markers across five instruction-tuned LLMs. The mappings vary substantially across models and do not follow a consistent ordering.

Figure 3: Estimated PT parameters (σ, λ, γ) at baseline and across four re-measurement rounds with epistemic markers. Parameter estimates drift considerably once linguistic uncertainty is introduced.

Figure 4: PT fitness measured by MAE (lower is better) and McFadden R² (higher is better). The fitted PT model captures LLM decision-making inconsistently across models and rounds.

🚀 Quick Start

Installation

git clone https://github.com/HKUST-KnowComp/MarPT.git
cd MarPT
pip install -r requirements.txt

Model Deployment

Start a vLLM server with your target model:

vllm serve Qwen/Qwen3-32B --port 8000

The experiments expect an OpenAI-compatible API at http://localhost:8000/v1 by default. You can override this with the VLLM_BASE_URL environment variable:

export VLLM_BASE_URL=http://your-server:8000/v1

Running an Experiment

Navigate to the directory of the stage you want to run (e.g., Stage 1 baseline):

cd risk

Configure the target model(s):

1. Open elicitation.py
2. Edit models_to_test to select your target model(s)
3. Optionally adjust base_url, sample_num, and batchsize

Run elicitation and process the results:

# Elicitation — raw outputs are saved under result/
python elicitation.py

# Processing — measured parameters are saved in processed/
python process.py > result.txt

Customizing Marker Substitution (Stage 3 only)

To customize how epistemic markers replace numerical probabilities:

1. Open risk_marker/prompt.py
2. Modify the function safe_sub as needed

📝 Notes

• The generator/ module provides a unified VLLMGenerator class used by all three stages.
  • risk/ and risk_marker/ use chat completion (/v1/chat/completions) with multi-turn conversations.
  • marker/ uses text completion (/v1/completions) with raw prompts.
• For Qwen3 models, thinking mode is automatically disabled via chat_template_kwargs.
• For QwQ models, a system message suppressing reasoning is automatically prepended.
• Ensure the vLLM model server is running before starting any elicitation.

📚 Citing this work

If you use this codebase in your research, please cite:

@misc{wang2025rethinkingprospecttheoryllms,
      title={Rethinking Prospect Theory for LLMs: Revealing the Instability of Decision-Making under Epistemic Uncertainty},
      author={Rui Wang and Qihan Lin and Jiayu Liu and Qing Zong and Tianshi Zheng and Dadi Guo and Haochen Shi and Peixuan Han and Weiqi Wang and Yangqiu Song},
      year={2025},
      eprint={2508.08992},
      archivePrefix={arXiv},
      primaryClass={cs.AI},
      url={https://arxiv.org/abs/2508.08992},
}

📄 License

MIT