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

Rui Wang; Qihan Lin; Jiayu Liu; Qing Zong; Tianshi Zheng; Dadi Guo; Haochen Shi; Peixuan Han

cs.AIAug 12, 2025

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

Authors: Rui Wang, Qihan Lin, Jiayu Liu, Qing Zong, Tianshi Zheng, Dadi Guo, Haochen Shi, Peixuan Han, +2 more

Organizations: Hong Kong University of Science and Technology · Huazhong University of Science and Technology · University of Illinois Urbana-Champaign

Abstract

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. Although recent studies have developed frameworks to estimate PT parameters for Large Language Models (LLMs), few have examined whether PT itself adequately describes LLM decision-making behavior. To address these gaps, we develop a streamlined workflow grounded in a classic behavioral economics experimental paradigm. First, we estimate PT parameters and evaluate how well the resulting model captures LLM decision-making behavior. We then 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. 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 sensitive to epistemic uncertainty. The findings caution against the deployment of PT-based frameworks in real-world applications where epistemic ambiguity is prevalent, giving valuable insights in behaviour interpretation and future alignment direction for LLM decision-making.

Figures & tables

Figure 1: An overview of our three-stage experiment. Stage 1 fits PT parameters from binary choices with precise probabilities. Stage 2 estimates each marker’s internal probability from the point where options K and U are chosen equally. Stage 3 substitutes probabilities with markers to measure the effect of linguistic uncertainty markers.

Panel of Figure 2 — Figure 2: Visual illustration of the three PT parameters ( $\sigma$ , $\lambda$ , $\gamma$ ). Each parameter is shown with its meaning and an interpretation of its directional significance.

No.	Epistemic Marker	Probability Mapping by Human
1	almost certain	95%
2	highly likely	90%
3	very likely	90%
4	likely	80%
5	probable	70%
6	somewhat likely	70%

Table 1: Epistemic markers and human probability mappings from Belem et al. (2024) .

Figure 3: Illustration of calculating $p_{mapping}$ . We use linear interpolation via similar triangles.

Model	$\sigma$	$\lambda$	$\gamma$	MAE $\downarrow$	R 2 $\uparrow$
Human	0.670	2.630	0.685	-	-
Llama-3.1-8B-Instruct	0.585	0.010	0.753	0.332	0.092
Mistral-7B-Instruct-v0.3	0.534	0.570	0.577	0.155	0.132
Qwen2.5-7B-Instruct	0.429	0.010	3.645	0.047	0.116
Qwen2.5-14B-Instruct	0.503	1.909	0.896	0.257	0.067
Qwen2.5-32B-Instruct	0.598	1.213	0.867	0.161	0.225

Table 2: Baseline Prospect Theory (PT) parameter estimation across evaluated LLMs. Human benchmarks are sourced from ( Tanaka et al., 2010 ) . For reasoning-capable models ( GPT-5-Mini and Gemini-2.5-Flash ), we employ chain-of-thought prompts while explicitly prohibiting expected-value calculations. Bolded entries denote a reliable fit based on the criteria of

MAE\leq 0.20

and

R^{2}\geq 0.10

Figure 4: Probability mapping of different models for different markers.

Figure 5: PT parameters estimated across rounds. Baseline corresponds to the first stage; subsequent rounds show parameter fluctuations.

Figure 6: PT performance across rounds. Baseline represents initial PT fitness; MAE and McFadden $R^{2}$ vary considerably in later rounds.

Appendix figures & tables15 assets

Supplementary material from the paper’s appendix.

Appendix

Hyperparameter	Value
Temperature	0.7
Maximum new tokens	8
History length	10
Number of lottery rounds	35

Appendix

Table 3: Key hyperparameters for model generation

Setup	Description	Value
$\eta$	Number of repeated samples per lottery question	$256$
$M$	Number of lottery-choice questions	$35$
$\alpha$	Significance level for confidence intervals	$0.05$
$1-\alpha$	Confidence level	$0.95$

Appendix

Table 4: Experiment setup hyperparameters used in decision-making behavior evaluation.

Model	30%	70%	10%	90%
Qwen2.5-7B-Instruct	uncertain	almost certain	somewhat likely	highly likely
Llama3.1-8B-Instruct	likely	almost certain	very unlikely	almost certain
Mistral-7B-Instruct-v0.3	very unlikely	highly likely	highly unlikely	almost certain
Qwen2.5-14B-Instruct	somewhat unlikely	highly likely	very unlikely	almost certain
Qwen2.5-32B-Instruct	somewhat unlikely	probable	somewhat likely	almost certain

Appendix

Table 5: Marker Replacement Rules for Different Models. This is determined for introducing the least numeric differences, and balancing model and human interpretations.

	Option K		Option U
Lottery	30%	70%	10%	90%
1	40	10	68	5
2	40	10	75	5
3	40	10	83	5
4	40	10	93	5
5	40	10	106	5

Appendix

Table 6: Series 1: both options are gains.

	Option K		Option U
Lottery	90%	10%	70%	30%
1	40	30	54	5
2	40	30	56	5
3	40	30	58	5
4	40	30	60	5
5	40	30	62	5

Appendix

Table 7: Series 2: both options are gains.

	Option K		Option U
	50%	50%	50%	50%
Lottery	Win	Lose	Win	Lose
1	25	4	30	21
2	4	4	30	21
3	1	4	30	21
4	1	4	30	16

Appendix

Table 8: Series 3 both options have gains and losses.

Panel of Figure 7 — Figure 7: Templates for prompts used in the probability mapping and Prospect Theory estimation tasks. The design includes an initial instruction, task-specific lottery descriptions, and a fixed closing instruction to ensure direct model responses without reasoning.

Figure 8: An example of non-monotonic result with multiple switching points. This result comes from marker “It’s undoubtedly to” with Qwen2.5-7B-Instruct model over 256 trials. The blue line shows counts of option K selections, and the yellow dashed line marks half the trials. The crosses denote switching points.

Panel of Figure 9 — Figure 9: An example of mapping high-certainty markers to low probablity. In this case, Qwen2.5-7B-Instruct preferred option K when $p=15\%$ and option U was described using “It’s extremely certain to” , implying a far lower internal probability than expected.

Model	Top 7 Epistemic Markers
Model	almost certain	highly likely	very likely	likely	probable	somewhat likely	possible
Llama-3.1-8B-Instruct	87.92	56.04	58.00	41.80	44.23	36.71	36.29
Mistral-7B-Instruct-v0.3	96.80	67.89	63.10	57.50	87.22	48.98	52.16
Qwen2.5-7B-Instruct	82.71	67.00	67.06	0 4.78	0 3.44	0 8.93	0 4.51
Qwen2.5-14B-Instruct	91.56	55.00	54.10	42.38	26.51	32.47	38.38
Qwen2.5-32B-Instruct	97.50	95.08	82.82	65.00	54.74	46.08	55.00

Appendix

Table 9: Switching probabilities (%) for top 7 epistemic markers. For GPT-5-Mini and Gemini-2.5-Flash , we allow reasoning while prohibiting expected-value calculation. See 10 for bottem 7 markers mappings.

Model	Bottom 7 Epistemic Markers
Model	uncertain	somewhat unlikely	unlikely	not likely	doubtful	very unlikely	highly unlikely
Llama-3.1-8B-Instruct	35.49	33.71	33.49	36.91	33.65	31.30	32.83
Mistral-7B-Instruct-v0.3	48.08	40.15	38.27	30.93	34.03	29.47	27.88
Qwen2.5-7B-Instruct	35.58	27.24	19.90	27.70	25.69	18.37	19.32
Qwen2.5-14B-Instruct	29.03	26.45	19.10	20.82	13.04	10.94	10.52
Qwen2.5-32B-Instruct	0 2.98	21.89	0 3.33	0 3.08	0 3.42	0 2.77	0 2.51

Appendix

Table 10: Switching probabilities (%) for bottom 7 epistemic markers. Experiment setup is the same as Table 9 .

Model	$\sigma$ (95% CI)
Model	baseline	round1	round2	round3	round4
Llama-3.1-8B-Instruct	$0.585\,(0.578,0.592)$	$0.605\,(0.599,0.612)$	$0.573\,(0.566,0.580)$	$0.463\,(0.455,0.473)$	$0.593\,(0.585,0.602)$
Mistral-7B-Instruct-v0.3	$0.534\,(0.526,0.543)$	$0.566\,(0.558,0.574)$	$0.571\,(0.564,0.580)$	$0.384\,(0.370,0.399)$	$0.444\,(0.431,0.454)$
Qwen2.5-7B-Instruct	$0.429\,(0.415,0.445)$	$0.010\,(0.010,0.074)$	$0.250\,(0.232,0.275)$	$0.010\,(0.010,0.071)$	$0.344\,(0.332,0.359)$
Qwen2.5-14B-Instruct	$0.503\,(0.495,0.511)$	$0.444\,(0.434,0.454)$	$0.409\,(0.398,0.421)$	$0.563\,(0.555,0.573)$	$0.589\,(0.581,0.600)$
Qwen2.5-32B-Instruct	$0.598\,(0.591,0.605)$	$0.569\,(0.561,0.576)$	$0.564\,(0.556,0.572)$	$0.647\,(0.640,0.655)$	$0.607\,(0.599,0.615)$

Appendix

Table 11:

\sigma

estimates with 95% confidence intervals across different rounds for each model.

Model	$\lambda$ (95% CI)
Model	baseline	round1	round2	round3	round4
Llama-3.1-8B-Instruct	$0.010\,(0.010,0.125)$	$0.010\,(0.010,0.117)$	$0.010\,(0.010,0.130)$	$0.010\,(0.010,0.168)$	$0.010\,(0.010,0.112)$
Mistral-7B-Instruct-v0.3	$0.570\,(0.453,0.688)$	$0.010\,(0.010,0.132)$	$0.010\,(0.010,0.135)$	$2.260\,(2.060,2.445)$	$0.267\,(0.105,0.414)$
Qwen2.5-7B-Instruct	$0.010\,(0.010,0.584)$	$4.000\,(0.010,4.000)$	$4.000\,(3.526,4.000)$	$4.000\,(0.010,4.000)$	$4.000\,(3.736,4.000)$
Qwen2.5-14B-Instruct	$1.909\,(1.801,2.013)$	$1.919\,(1.784,2.070)$	$2.851\,(2.675,3.023)$	$2.191\,(2.094,2.295)$	$2.531\,(2.409,2.648)$
Qwen2.5-32B-Instruct	$1.213\,(1.133,1.295)$	$1.340\,(1.250,1.423)$	$0.953\,(0.866,1.036)$	$2.013\,(1.945,2.090)$	$1.815\,(1.736,1.905)$

Appendix

Table 12:

\lambda

estimates with 95% confidence intervals across different rounds for each model.

Model	$\gamma$ (95% CI)
Model	baseline	round1	round2	round3	round4
Llama-3.1-8B-Instruct	$0.753\,(0.740,0.767)$	$0.750\,(0.737,0.762)$	$0.755\,(0.741,0.768)$	$1.020\,(0.994,1.053)$	$1.478\,(1.443,1.517)$
Mistral-7B-Instruct-v0.3	$0.577\,(0.565,0.590)$	$0.564\,(0.554,0.574)$	$0.535\,(0.527,0.545)$	$1.413\,(1.300,1.564)$	$1.332\,(1.266,1.414)$
Qwen2.5-7B-Instruct	$3.645\,(3.501,3.783)$	$1.156\,(0.010,4.000)$	$0.985\,(0.870,1.174)$	$1.035\,(0.010,3.498)$	$0.987\,(0.926,1.053)$
Qwen2.5-14B-Instruct	$0.896\,(0.875,0.919)$	$0.933\,(0.905,0.967)$	$0.983\,(0.944,1.023)$	$1.455\,(1.414,1.503)$	$1.742\,(1.693,1.803)$
Qwen2.5-32B-Instruct	$0.867\,(0.851,0.884)$	$0.778\,(0.762,0.793)$	$0.812\,(0.797,0.828)$	$0.614\,(0.605,0.623)$	$0.664\,(0.653,0.674)$

Appendix

Table 13:

\gamma

estimates with 95% confidence intervals across different rounds for each model.

Model	MAE					McFadden $R^{2}$
	baseline	round1	round2	round3	round4	baseline	round1	round2	round3	round4
Llama-3.1-8B-Instruct	0.332	0.320	0.326	0.242	0.155	0.092	0.121	0.090	0.082	0.335
Mistral-7B-Instruct-v0.3	0.155	0.202	0.196	0.067	0.075	0.132	0.162	0.190	0.056	0.130
Qwen2.5-7B-Instruct	0.047	0.125	0.159	0.387	0.157	0.116	0.000	0.011	-0.001	0.032
Qwen2.5-14B-Instruct	0.257	0.152	0.069	0.150	0.157	0.067	0.070	0.075	0.227	0.336
Qwen2.5-32B-Instruct	0.161	0.127	0.129	0.224	0.256	0.225	0.195	0.211	0.139	0.088

Appendix

Table 14: Mean absolute error (MAE) and McFadden

R^{2}

across different rounds for each model.

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Large Language Models (LLMs) are predominantly governed by probabilistic frameworks in which the sum of outcome probabilities is constrained to unity. This architectural limitation, often imposed by Softmax layers, leads to a collapse of uncertainty that makes it difficult to differentiate between epistemic uncertainty, paradox, and vagueness. We present an empirical investigation of the application of Neutrosophic Logic, a framework that treats Truth (T), Indeterminacy (I), and Falsity (F) as three independent dimensions, to model epistemic states in LLMs. We conducted experiments on a family of four OpenAI GPT models across five linguistic phenomena: logical paradoxes, epistemic ignorance, vagueness, ethical contradictions, and future contingencies, under three prompting strategies: neutrosophic, probabilistic, and entropy-derived. Our findings reveal that the neutrosophic approach, by allowing T+I+F > 1, a state we term hyper-truth, provides a richer representation of a model's internal state. In 35% of evaluations, hyper-truth emerged spontaneously, predominantly under ethical contradiction and logical paradox. We demonstrate that this approach preserves truth values in fuzzy contexts and offers a robust method for identifying and quantifying internal model conflict. We conclude that the integration of neutrosophic evaluation layers is a critical step toward more transparent, reliable, and ethically aware AI systems.

Abstract

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