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

2026-07-16 · Source: Computation and Language · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, quick

Summary

A new evaluation method, "Partition, Prompt, Aggregate," investigates whether large language model (LLM) estimates adhere to basic probabilistic identities, specifically the law of total probability. This work uses binary trees to recursively partition populations into fine-grained subpopulations. LLMs are then prompted with verbalized subpopulation descriptions, and the resulting estimates are aggregated back to population-level estimates for comparison across varying granularities. Applying this protocol across various problem domains and advanced frontier models revealed widespread violations of fundamental consistency properties. An in-depth study of persona prompting uncovered a "macro fallacy": estimates reconstructed from more fine-grained subpopulation responses frequently align better with human reference data than direct population-level estimates. This effect remains consistent across different tree structures and estimation tasks, and implicit prompting can partially recover it. These findings indicate that models possess relevant subpopulation knowledge but struggle to reliably propagate it into aggregate estimates, establishing statistical self-consistency as an unsaturated, reference-free LLM evaluation criterion.

Key takeaway

For machine learning engineers evaluating LLM reliability, you should integrate statistical self-consistency as a critical, reference-free evaluation metric. Recognize that direct population-level estimates from LLMs may be less accurate than those aggregated from fine-grained subpopulation responses, a phenomenon termed the "macro fallacy." Consider designing prompting strategies that leverage subpopulation knowledge, potentially through implicit prompting, to improve overall estimate accuracy and ensure probabilistic consistency in your applications.

Key insights

LLMs widely violate statistical self-consistency, often performing better when aggregating fine-grained subpopulation estimates than direct population estimates.

Principles

• LLMs struggle with probabilistic consistency.
• Fine-grained prompts can reveal hidden knowledge.
• Direct population estimates can be less accurate.

Method

The "Partition, Prompt, Aggregate" protocol involves recursively partitioning populations using binary trees, prompting LLMs with subpopulation descriptions, aggregating estimates, and comparing them across granularities.

In practice

• Evaluate LLMs using statistical self-consistency.
• Consider fine-grained prompting for accuracy.
• Test implicit prompting for recovery.

Topics

• Statistical Self-Consistency
• Large Language Models
• Prompt Engineering
• Macro Fallacy
• Probabilistic Consistency
• LLM Evaluation

Best for: Research Scientist, AI Engineer, AI Scientist, Machine Learning Engineer, NLP Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by Computation and Language.