Humans and LLMs Diverge on Probabilistic Inferences
Organizations: McGill University · Mila – Quebec AI Institute · University of Vienna · FNRS – UCLouvain ·
Abstract
Human reasoning often involves working over limited information to arrive at probabilistic conclusions. In its simplest form, this involves making an inference that is not strictly entailed by a premise, but rather only likely given the premise. While reasoning LLMs have demonstrated strong performance on logical and mathematical tasks, their behavior on such open-ended, non-deterministic inferences remains largely unexplored. We introduce ProbCOPA, a dataset of 210 handcrafted probabilistic inferences in English, each annotated for inference likelihood by 25--30 human participants. We find that human responses are graded and varied, revealing probabilistic judgments of the inferences in our dataset. Comparing these judgments with responses from eight state-of-the-art reasoning LLMs, we show that models consistently fail to produce human-like distributions. Finally, analyzing LLM reasoning chains, we find evidence of a common reasoning pattern used to evaluate such inferences. Our findings reveal persistent differences between humans and LLMs, and underscore the need to evaluate reasoning beyond deterministic settings.
Figures & tables
| Model | Premise | Hypothesis | Reasoning Chain Extract |
|---|---|---|---|
| Kimi-K2-Thinking | The tire on my bike was flat. | I pumped air into the tire. | …When a bike tire is flat, the most common and logical action is to pump air into it… However, there are other possibilities : … They might not fix it at all … They might replace the tube/tire entirely … they might take it to a shop … |
| DeepSeek-R1 | The girl looked pale. | Her father read her a story. | …This is an action a parent might take to comfort a child… However, it’s not the only response. The father might giver her medicine, ask what’s wrong, take her to a doctor, or just let her rest … |
| GLM-4.6 | The man anticipated the team’s victory. | He made a bet with his friends. | …when people anticipate a victory for a team they support, they might be more inclined to bet on that outcome… However … They might not be gamblers … They might not have money to bet … They might be satisfied with just watching the game … |
Appendix figures & tables18 assets
Supplementary material from the paper’s appendix.
Appendix
| Model Name | Exact Model Version |
|---|---|
| Gemini-3 | gemini-3-pro-preview |
| GPT-5 | gpt-5-2025-08-07 |
| Claude Sonnet-4.5 | claude-sonnet-4-5-20250929 |
| Qwen3 | Qwen3-235B-A22B-Thinking-2507 |
| Kimi-K2 | Kimi-K2-Thinking |
| GLM-4.6 | GLM-4.6 |
| Reasoning Effort | Proportion of non-Empty Reasoning Summaries | Range of Total Count of Output Tokens | Mean Differential Entropy of Responses | Median Number of Unique Responses |
| low | 0.000 | 10–10 | -0.486 | 1.0 |
| medium | 0.000 | 10–10 | -0.667 | 1.0 |
| high | 0.198 | 10–250 | -0.296 | 1.0 |
| Persona Type | Persona Prompt Examples |
|---|---|
| Demographic | You are a 23-year-old female barista in Ottawa, who is saving up to backpack across Europe. Your first language is English. |
| You are a 58-year-old male factory worker in Detroit, who is nearing retirement after three decades in the auto industry. Your first language is English. | |
| You are a 36-year-old male taxi driver in Birmingham, who works night shifts to have more time with his young children during the day. Your first language is English. | |
| Psychological | You balance curiosity with pragmatism, comfortable with both the familiar and the new. You are dependable and organized, often making plans to reach your goals. You feel comfortable in both quiet and social settings, adapting as needed. You are caring and cooperative, often attuned to the feelings of those around you. You experience typical ups and downs but manage emotions with balance. |
| You are imaginative and drawn to creativity, often seeking new ways to challenge your thinking. You manage responsibilities reasonably well without being overly rigid. You feel comfortable in both quiet and social settings, adapting as needed. You balance kindness with self-interest, showing empathy without overextending yourself. You sometimes feel self-doubt and worry, but this also makes you sensitive to others’ struggles. |
| Reasoning chain length (tokens) Differential entropy of human likelihood scores | Reasoning chain length (tokens) Human response time (log-transformed and -scored) | |||
| Model | Spearman’s | -value | Spearman’s | -value |
| GPT-5 | 0.30 | 7.06e-06 | 0.17 | 1.19e-02 |
| Claude Sonnet-4.5 | 0.18 | 9.61e-03 | 0.12 | 8.74e-02 |
| DeepSeek-R1 | 0.36 | 6.54e-08 | 0.18 | 9.85e-03 |
| Gemini-3 | 0.50 | 2.10e-14 | 0.18 | 9.86e-03 |
| Kimi-K2 | 0.33 | 1.05e-06 | 0.24 | 4.44e-04 |
LLM Reasoning
Large language model reasoning studies how models solve multi-step problems, verify intermediate steps, and use computation or tools reliably.
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