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Large Language Models (LLMs) have been used as experts to infer causalgraphs, often by repeatedly applying a pairwise prompt that asks about thecausal relationship of each variable pair. However, such experts, includinghuman domain experts, cannot distinguish between direct and indirect effectsgiven a pairwise prompt. Therefore, instead of the graph, we propose thatcausal order be used as a more stable output interface for utilizing expertknowledge. Even when querying a perfect expert with a pairwise prompt, we showthat the inferred graph can have significant errors whereas the causal order isalways correct. In practice, however, LLMs are imperfect experts and we findthat pairwise prompts lead to multiple cycles. Hence, we propose the tripletmethod, a novel querying strategy that introduces an auxiliary variable forevery variable pair and instructs the LLM to avoid cycles within this triplet.It then uses a voting-based ensemble method that results in higher accuracy andfewer cycles while ensuring cost efficiency. Across multiple real-world graphs,such a triplet-based method yields a more accurate order than the pairwiseprompt, using both LLMs and human annotators. The triplet method enhancesrobustness by repeatedly querying an expert with different auxiliary variables,enabling smaller models like Phi-3 and Llama-3 8B Instruct to surpass GPT-4with pairwise prompting. For practical usage, we show how the expert-providedcausal order from the triplet method can be used to reduce error in downstreamgraph discovery and effect inference tasks.

Causal Order: The Key to Leveraging Imperfect Experts in Causal Inference