SEU Sensitivity

Modeling Sensitivity to Subjective Expected Utility Maximization

Author

Jeff Helzner

Published

May 12, 2026

0.1 Introduction

This project provides a Bayesian framework for modeling and analyzing decision-making behavior through the lens of Subjective Expected Utility (SEU) theory. We develop computational tools for measuring an agent’s sensitivity to SEU maximization—captured by a parameter α that governs how consistently agents maximize expected utility.

0.2 Report Series

0.2.1 Foundational Reports

These reports establish the theoretical and methodological foundations:

  1. Abstract Formulation — Mathematical specification and key theoretical properties
  2. Concrete Implementation — Stan model implementation details
  3. Prior Analysis — Prior predictive analysis and prior selection
  4. Parameter Recovery — Validation that parameters can be recovered from data
  5. Adding Risky Choices — Extension to model m_1 for utility identification
  6. SBC Validation — Simulation-based calibration results
  7. Generalizing Sensitivity — Generalized models m_2 and m_3
  8. Hierarchical Formulation — Hierarchical extension for population-level inference
  9. Hierarchical Implementation — Stan implementation and validation of hierarchical models
  10. Hierarchical Prior Analysis — Prior predictive analysis for h_m01
  11. Hierarchical Parameter Recovery — Recovery validation for the hierarchical model
  12. Hierarchical SBC Validation — Simulation-based calibration for h_m01

0.2.2 Application Reports

0.2.2.1 Temperature Study

  1. Initial Results — How LLM temperature affects estimated SEU sensitivity

0.2.2.2 Temperature Study: EU Prompt

  1. EU Prompt Study — Effect of explicit EU-maximization framing on sensitivity

0.2.2.3 Temperature Study: Risky Alternatives

  1. Risky Alternatives Extension — Risky choice data for utility identification across temperatures

0.2.2.4 Ellsberg Study

  1. Ellsberg Study — Claude 3.5 Sonnet on Ellsberg urn gambles

0.2.2.5 Factorial Cells

0.2.2.6 Factorial Synthesis

  1. 2×2 Factorial Analysis — Cross-LLM × cross-task synthesis

0.3 Key Insights

NoteThe Sensitivity Parameter α

The parameter α has a natural interpretation:

  • α → 0: Random choice (uniform over alternatives)
  • α → ∞: Perfect SEU maximization (deterministic optimal choice)
  • Intermediate α: Probabilistic choice with tendency toward higher-SEU alternatives

With utilities normalized to [0,1], α represents the log-odds change per unit of standardized SEU difference.

ImportantA Central Finding

Decisions under uncertainty alone cannot fully identify the utility function—utilities and subjective probabilities are confounded. The foundational reports demonstrate that incorporating risky choices (with known probabilities) resolves this identification problem, following the Anscombe-Aumann approach from classical decision theory.

0.4 Getting Started

See the GitHub repository for installation instructions and code.

0.5 Citation

If you use this work, please cite:

Helzner, J. (2026). SEU Sensitivity: A Bayesian Framework for Modeling 
Decision-Making Sensitivity. https://github.com/jeffhelzner/seu-sensitivity

Reuse

Citation

BibTeX citation:
@online{helzner2026,
  author = {Helzner, Jeff},
  title = {SEU {Sensitivity}},
  date = {2026-05-12},
  url = {https://jeffhelzner.github.io/seu-sensitivity/},
  langid = {en}
}
For attribution, please cite this work as:
Helzner, Jeff. 2026. “SEU Sensitivity.” SEU Sensitivity Project, May 12. https://jeffhelzner.github.io/seu-sensitivity/.