Rethinking Prospect Theory for LLMs: Revealing the Instability of Decision-Making under Epistemic Uncertainty

Real-world decision-making often involves uncertainty expressed in linguistic rather than numerical terms, and Prospect Theory (PT) provides a classic framework for modeling human behavior under such uncertainty. This study develops a streamlined workflow to evaluate how Prospect Theory adequately describes Large Language Model (LLM) decision-making behavior and reveals the instability of these parameters when LLMs are exposed to epistemic uncertainty. The findings caution against deploying PT-based frameworks in real-world applications where epistemic ambiguity is prevalent, suggesting that LLMs do not exhibit universal Prospect-Theory-like behavior and their risk tendencies are likely not robust under linguistic uncertainty.

The core methodology involves a three-stage experiment designed to test the robustness of PT parameters against linguistic uncertainty.

1. First, the researchers estimate PT parameters and evaluate how well the resulting model captures LLM decision-making behavior by fitting PT parameters from binary choices with precise probabilities.

2. Second, they derive probability mappings for epistemic markers in the same context and inject them into prompts to examine the stability of PT parameters under linguistic uncertainty. This stage involves having LLMs make binary choices between numerical probabilities and epistemic markers to infer the model’s implicit probabilistic interpretation of those uncertainty expressions under the same context.

3. Finally, they re-assess model behavior on the original decision tasks, now framed using epistemic markers grounded in their inferred probability values, to directly evaluate the impact of epistemic uncertainty on decision-making.

The framework is built upon classic behavioral economics to establish a reliable baseline for PT parameter measurement.

(Note: The paper details that they adopt a three-series lottery-choice experiment developed from Tanaka et al. (2010) to get a reliable PT parameter measurement, where Series 1 and 2 elicit risk preference and probability weighting, while Series 3 is designed for loss aversion.)

The evaluation metrics used to assess model fit include:

(Note: The researchers quantify goodness-of-fit using McFadden pseudoR2 (McFadden, 1977), defined as R2 McFadden = 1 − LPT/Lnull, and the mean absolute error (MAE) between the actual probability pactual and the predicted probability ppred of choosing option K.)

The study investigates how epistemic markers influence LLM decision-making across varying degrees of linguistic uncertainty.

The researchers establish a No. Epistemic Marker Probability Mapping by Human to define how humans map verbal expressions to numerical probabilities, which serves as the basis for subsequent experiments. They then perform Probability interpolation using a slope formula to estimate an inferred probability mapping (pmapping) for each marker based on where the model reaches an implied probability of 0.5 (p0). This allows them to obtain a list of 14 probability values (one per marker) for each model, capturing how they semantically interpret verbal uncertainty in economic terms.

The results reveal key insights regarding the relationship between LLM scale, PT adherence, and epistemic uncertainty.

(Note: The findings show that Prospect Theory does not consistently perform well at explaining LLM decision behaviors, and that larger models exhibit more Prospect-Theorylike behavior, while loss aversion remains unstable.)

The study highlights several limitations:

1. Scale Dependency: PT-aligned behavior is not an inherent model capability, but rather emerges only in models with sufficient parameter scale.

2. Representational Divergence: LLMs exhibit severe cross-model divergence in absolute probability mappings, even when capturing stable ordinal semantics across models.

3. Parameter Instability: The introduction of linguistic uncertainty profoundly destabilizes LLMs, rendering them unable to maintain theoretically coherent, stable, or interpretable PT parameters, revealing representational non-invariance.

The instability is further detailed by examining model-specific effects on PT fitness across four experimental rounds.

The analysis shows that while risk preference remains relatively stable despite marker substitution, loss aversion and probability weighting shift more substantially under these conditions. Specifically, changes in λ suggest models do not preserve the same loss sensitivity when equivalent uncertainty is expressed through linguistic markers rather than numerical probabilities. Furthermore, drift under semantically matched substitutions reveals non-invariant decision-making: models alter revealed preferences when equivalent uncertainty is expressed differently. The conclusion is that epistemic markers are not merely interchangeable verbal forms of numerical probabilities, but can directly affect the internal preference structure revealed by LLMs.

The study concludes with a strong recommendation for future system design and alignment.

The paper cautions against the uncritical deployment of PT-based frameworks to model or predict LLM behaviors in real-world applications where epistemic ambiguity is ubiquitous. It suggests that for safety-critical applications, "epistemic uncertainty must be strictly translated into standardized numeric probabilities, or models must be explicitly aligned via persona-prompting to enforce desired risk profiles.

Here are specific improvements for AI systems based on the findings of this research, categorized by technical capability:

)1. Enhanced Robustness Against Linguistic Ambiguity (Epistemic Uncertainty)

LLMs should be equipped with a mechanism that recognizes and explicitly quantifies epistemic markers (e.g., likely, somewhat unlikely) as distinct from numerical probabilities during decision-making processes, rather than treating them as direct substitutes for numbers.

)2. Dynamic Parameter Calibration for Decision-Making

The system should implement a dynamic calibration layer that adjusts its internal Prospect Theory parameters (Risk Preference, Loss Aversion, and Probability Weighting) in real-time based on the linguistic context of the prompt. This prevents the observed Parameter Instability where equivalent uncertainty expressed differently causes drastic shifts in preference structure.

)3. Scale-Dependent Confidence Thresholds

For safety-critical or high-stakes decisions (e.g., financial risk assessment, medical triage), the system should utilize a confidence threshold that is explicitly scaled with model size and robustness metrics (like McFadden R2 and MAE). Decisions based on PT frameworks should be flagged as Unreliable if the model falls below a predetermined scale/robustness benchmark, preventing deployment of models exhibiting unstable decision-making.

)4. Contextual Uncertainty Translation Module

Develop a dedicated module that maps linguistic uncertainty markers to normalized probability distributions (using the derived model-specific mappings). This module should be used as an intermediary step: instead of feeding raw text prompts into the LLM's decision engine, the system first translates the epistemic language into a standardized numerical probability space before applying PT logic.

)5. Explicit Persona/Constraint Enforcement for Alignment

For applications requiring guaranteed risk profiles (e.g., regulatory compliance), systems must utilize explicit persona prompting or constraint rules to force models toward desired risk attitudes (e.g., forcing high loss aversion in financial contexts). This addresses the finding that native LLMs lack stable PT adherence without external conditioning.

)Improved AI System Capabilities:

The improved system will transition from a model that simply guesses based on statistical artifacts to a system capable of:

1. Predicting how its own decision-making parameters will shift when faced with ambiguous, natural language inputs.

2. Maintaining decision stability across varying linguistic representations of uncertainty (e.g., handling both highly likely and probable without catastrophic shifts).

3. Self-assessing the reliability of its own risk estimation framework before making a high-stakes choice, effectively acting as a meta-cognitive layer that warns when its underlying decision model is breaking down due to linguistic noise.