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Seeing Through Risk: A Symbolic Approximation of Prospect Theory

Ali Arslan Yousaf, Umair Rehman, Muhammad Umair Danish

TL;DR

The paper addresses the mismatch between traditional expected utility theory and observed risk-taking behaviors by proposing a symbolic prospect-theoretic framework. It replaces opaque utility curves with interpretable, PT-aligned features in a logistic decision rule and uses effect-size guided feature selection to ensure data efficiency and theoretical relevance. Empirical validation on synthetic data shows the Symbolic Logistic Model reproduces framing and loss-aversion effects with interpretable coefficients and superior predictive performance compared to a Black-box logistic model and a brittle parametric CPT estimator. The approach offers a practical, transparent alternative for cognitive modeling and AI-safety applications, with potential impact on economic policy analysis and risk-sensitive decision-making.

Abstract

We propose a novel symbolic modeling framework for decision-making under risk that merges interpretability with the core insights of Prospect Theory. Our approach replaces opaque utility curves and probability weighting functions with transparent, effect-size-guided features. We mathematically formalize the method, demonstrate its ability to replicate well-known framing and loss-aversion phenomena, and provide an end-to-end empirical validation on synthetic datasets. The resulting model achieves competitive predictive performance while yielding clear coefficients mapped onto psychological constructs, making it suitable for applications ranging from AI safety to economic policy analysis.

Seeing Through Risk: A Symbolic Approximation of Prospect Theory

TL;DR

The paper addresses the mismatch between traditional expected utility theory and observed risk-taking behaviors by proposing a symbolic prospect-theoretic framework. It replaces opaque utility curves with interpretable, PT-aligned features in a logistic decision rule and uses effect-size guided feature selection to ensure data efficiency and theoretical relevance. Empirical validation on synthetic data shows the Symbolic Logistic Model reproduces framing and loss-aversion effects with interpretable coefficients and superior predictive performance compared to a Black-box logistic model and a brittle parametric CPT estimator. The approach offers a practical, transparent alternative for cognitive modeling and AI-safety applications, with potential impact on economic policy analysis and risk-sensitive decision-making.

Abstract

We propose a novel symbolic modeling framework for decision-making under risk that merges interpretability with the core insights of Prospect Theory. Our approach replaces opaque utility curves and probability weighting functions with transparent, effect-size-guided features. We mathematically formalize the method, demonstrate its ability to replicate well-known framing and loss-aversion phenomena, and provide an end-to-end empirical validation on synthetic datasets. The resulting model achieves competitive predictive performance while yielding clear coefficients mapped onto psychological constructs, making it suitable for applications ranging from AI safety to economic policy analysis.

Paper Structure

This paper contains 23 sections, 16 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Prospect Theory Essentials
  4. Symbolic AI and Interpretability
  5. Effect-Size-Guided Feature Selection
  6. Symbolic Modeling Framework
  7. Symbolic Feature Definition
  8. Symbolic Logistic Equation
  9. Effect-Size Thresholding
  10. Parameter Estimation
  11. Empirical Simulations and Validation Results
  12. Synthetic Data Generation
  13. Model Specifications
  14. Evaluation Metrics
  15. Quantitative Results
  16. ...and 8 more sections

Figures (4)

  • Figure 1: Accuracy and AUC for each model on the test set. The Symbolic Logistic model outperforms others in both metrics. Interpretability scores are discussed in Table \ref{['tab:results']}.
  • Figure 2: Reflection effect in the symbolic model: higher risk preference in loss frames.
  • Figure 3: Estimated CPT value function. Shallow slope and $\hat{\lambda} < 1$ indicate weak loss aversion.
  • Figure 4: Estimated Prelec probability weighting function. $\hat{\gamma} = 2.0$ causes underweighting of most probabilities.