Partition, Prompt, Aggregate: Statistical Self-Consistency in Language Models

This paper tests whether language-model estimates obey the law of total probability. Using binary trees, the authors recursively partition populations, prompt models with verbalized subgroup descriptions, aggregate subgroup estimates with their priors, and compare the result with direct population-level estimates. Across domains and frontier models, the study reports widespread violations of statistical self-consistency. In persona-prompting experiments, it identifies a “macro fallacy”: estimates reconstructed from fine-grained subgroup responses are often closer to human reference data than direct aggregate estimates. The authors propose statistical self-consistency as a reference-free evaluation criterion and report that implicit prompting can partially recover the effect.