Mind the (DH) Gap! A Contrast in Risky Choices Between Reasoning and Conversational LLMs

1. Problem Statement

As Large Language Models (LLMs) are increasingly deployed as decision-support systems and autonomous agents, understanding their behavior under uncertainty is critical. However, existing literature offers conflicting accounts of LLM rationality: some studies suggest LLMs align with human behavioral biases (Prospect Theory), while others suggest they maximize expected utility.

The authors identify a gap in understanding how representation (explicit descriptions vs. outcome histories) and output format (requesting explanations) affect LLM decision-making. Specifically, they investigate whether LLMs exhibit the Description-Experience (D-E) gap observed in humans, where choices differ based on whether prospects are described explicitly or learned through experience (histories). Furthermore, they seek to determine if LLMs behave as rational agents, human-like agents, or a distinct third category.

2. Methodology

Experimental Design

The study employs a controlled, two-option risky-choice benchmark involving 20 frontier and open-weight LLMs (including GPT-4.1/5.1, Gemini-2.5, DeepSeek-R1/Chat, Claude-Haiku, Qwen, and Olmo series) and 360 human subjects.

The experiment manipulates two primary dimensions:

1. Prospect Representation:
   • Explicit (Description): Options are presented as probability-payoff pairs (e.g., "70% chance of $100").
   • Implicit (History/Experience): Options are presented as simulated sequences of past outcomes (e.g., 15 instances of $100 and 5 instances of $0 from 20 trials).
   • Note: The study uses sample sizes of 20 and 100 for histories.
2. Decision Rationale (Explanation):
   • No Explanation: Output only the choice.
   • Short Explanation: Output choice + one-sentence justification.
   • Math Explanation: Output choice + brief mathematical reasoning.

Baselines and Metrics

• References: Model behavior is compared against Human Subjects and an Economicus (a risk-neutral, expected payoff-maximizing rational agent).
• Behavioral Metrics:
  • Correlation: Pearson correlation between model choice probabilities across contexts.
  • Decisiveness: Entropy of decisions (how deterministic the model is).
  • Consistency: Sensitivity to order (order consistency), framing (gain vs. loss), and prompt type (prompt consistency).
• Interpretable Modeling: The authors fit a Dual-Beta Prospect Theory model (4 parameters: risk preference $\sigma$, probability weighting $\gamma$, and domain-specific decisiveness $\beta_{gain}$ and $\beta_{loss}$) to the data to quantify underlying risk preferences and determinism.

3. Key Contributions

1. Discovery of Two Distinct LLM Clusters: The study identifies a robust bifurcation in LLM behavior:
   • Reasoning Models (RMs): Models explicitly trained for mathematical reasoning (e.g., DeepSeek-R1, GPT-5.1, Qwen-Math).
   • Conversational Models (CMs): Standard instruction-tuned or chat-optimized models (e.g., GPT-4.1, DeepSeek-Chat, Claude-Haiku).
2. Quantification of the Description-History (DH) Gap: The paper defines and measures the DH gap in LLMs, showing that the gap is modest for RMs but significant for CMs.
3. Training Paradigm as a Differentiator: The authors demonstrate that mathematical reasoning training is the primary factor distinguishing RMs from CMs, rather than model size or general instruction tuning.
4. The "Explanation Paradox": Contrary to the intuition that more reasoning leads to better decisions, the study finds that short explanations often increase rationality (alignment with Economicus), while mathematical explanations can sometimes decrease rationality in CMs or induce instability in RMs.

4. Key Results

Behavioral Clustering

• RMs cluster tightly with the Economicus (correlation 0.86–1.0). They are largely invariant to prospect order, framing, and explanation type. They behave similarly whether prospects are explicit or implicit.
• CMs are distinct from both Humans and the Economicus. They are highly sensitive to order, framing, and explanation types.
• Humans are uncorrelated with the Economicus (correlation ~0.14) and show a different behavioral profile than both RM and CM clusters.

The Description-History (DH) Gap

• CMs: Exhibit a large DH gap. When switching from explicit to implicit (history) prospects, CMs shift dramatically toward human-like behavior and away from rational (Economicus) behavior.
• RMs: Exhibit a small DH gap. Their behavior remains stable and rational regardless of whether prospects are described or experienced via history.
• Human Subjects: Interestingly, humans become more like the Economicus when presented with implicit histories, which partially explains why RMs (which stay rational) correlate more highly with humans in implicit settings.

Impact of Explanations

• Short Explanations: Generally increase the rationality of models (higher correlation with Economicus).
• Math Explanations: Have heterogeneous effects. For CMs, they often induce verbosity without improving rationality. For some RMs, they cause significant behavioral shifts, sometimes reducing rationality compared to the "no explanation" baseline.

Training and Scale Analysis

• Math Reasoning: Open-weight models trained specifically for math (e.g., Qwen-Math, Olmo-Think) consistently fall into the RM cluster, exhibiting high decisiveness ($\beta \approx 1000$) and rationality ($\sigma, \gamma \approx 1$).
• Instruction Tuning: Standard instruction-tuned variants of the same base models fall into the CM cluster, showing lower decisiveness and higher sensitivity to framing.
• Scale: Larger models tend to be more Pareto-dominant (simultaneously more human-like and more economicus-like) than smaller counterparts, but the training objective (reasoning vs. conversation) remains the primary classifier.

5. Significance and Implications

• Taxonomy of LLMs: This work provides the first systematic behavioral taxonomy separating LLMs into "Reasoning" and "Conversational" categories based on economic decision-making, moving beyond simple performance benchmarks.
• AI Safety and Alignment: The findings suggest that deploying LLMs as economic agents requires careful selection of model types. RMs are preferable for tasks requiring consistent, rational decision-making under uncertainty, while CMs may introduce significant unpredictability and bias depending on how information is presented.
• Interface Design: The study highlights that the "DH gap" is a critical design consideration. Systems relying on LLMs must be aware that presenting data as a history of outcomes versus a statistical description can drastically alter the agent's choice, particularly for conversational models.
• Explainability: The results challenge the assumption that forcing LLMs to "think" (via math explanations) always improves decision quality. In some cases, it may degrade performance, suggesting that the type of explanation requested is a crucial hyperparameter for decision-support systems.

In conclusion, the paper argues that LLM economic behavior is not a monolithic property but is deeply contingent on the model's training lineage (specifically mathematical reasoning) and the interface design (representation and prompting).