Partition, Prompt, Aggregate: Statistical Self-Consistency in Language Models
2026-07-16 • Computation and Language
Computation and Language
AI summaryⓘ
The authors studied whether large language models (LLMs) give answers that follow basic probability rules when they learn from examples in text prompts. They tested if the models' predictions for groups split into smaller subgroups add up correctly to the bigger group's prediction. Their experiments showed that LLMs often break these consistency rules, meaning their overall answers don't always reflect their knowledge about smaller groups. They also found that when looking at fine details, the models' estimates matched humans better than their whole-group answers, revealing a gap in how models combine knowledge. This suggests a new way to check and improve LLMs based on statistical consistency.
In-context learningConditional inferenceLaw of total probabilityLarge language models (LLMs)Probability consistencySubpopulation estimationPersona promptingMacro fallacyStatistical self-consistencyPrompt engineering
Authors
Patrik Wolf, Thomas Kleine Buening, Andreas Krause, Celestine Mendler-Dünner
Abstract
In-context learning is commonly interpreted as a form of conditional inference, in which the prompt specifies a context and the model's output is treated as an estimate of the corresponding conditional distribution. If this interpretation holds, then LLM estimates should satisfy basic probabilistic identities. In particular, the law of total probability asserts that prior-weighted conditional distributions aggregate into population-level marginals over any valid partition of the population. In this work, we investigate to what extent LLM estimates adhere to this self-consistency principle. We use binary trees as an evaluation scaffold to recursively partition a population into increasingly fine-grained subpopulations. We then prompt LLMs with verbalized subpopulation descriptions in context, aggregate the resulting estimates back into population-level estimates, and compare them across partitions of varying granularity. Applying this protocol across problem domains and state-of-the-art frontier models, we show widespread violations of basic consistency properties. An in-depth study of persona prompting reveals a pattern we call the macro fallacy: estimates reconstructed from more fine-grained subpopulation responses are often better aligned with human reference data than direct population-level estimates. This effect persists across variations in tree structure and estimation task, and can be partially recovered through implicit prompting. Together, these findings suggest that models possess relevant subpopulation knowledge but do not reliably propagate it into aggregate estimates. This gap establishes statistical self-consistency as an unsaturated, reference-free criterion for evaluating LLMs.