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Methods such as Inverse Constitutional AI (ICAI) attempt to improve interpretability by compressing datasets into short ``constitutions'' of natural-language principles. We argue this framing is under-specified: a flat list of principles is not yet an executable decision rule because it leaves principle composition implicit. We use the pairwise setting as a testbed to empirically characterize three open problems in constitutional methods. First, principle quality is hard to measure: coverage and accuracy are useful but incomplete proxies for end-to-end reconstruction. Second, \\emph{composition is ambiguous}: holding principles fixed, different executors (LLM judge versus majority vote) agree only $73\\%$ of the time. Third, \\emph{constitutions differ between LLMs}: cross","title":"Open Problems in Constitutional Preference Reconstruction","url":"https://arxiv.org/abs/2606.30116","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.30116v1 Announce Type: new \nAbstract: Pairwise preference data is widely used for training and evaluating language models (e.g., RLHF), but each datapoint records a \\emph{choice}, not the rationale behind it. Methods such as Inverse Constitutional AI (ICAI) attempt to improve interpretability by compressing datasets into short ``constitutions'' of natural-language principles. We argue this framing is under-specified: a flat list of principles is not yet an executable decision rule because it leaves principle composition implicit. We use the pairwise setting as a testbed to empirically characterize three open problems in constitutional methods. First, principle quality is hard to measure: coverage and accuracy are useful but incomplete proxies for end-to-end reconstruction. Second, \\emph{composition is ambiguous}: holding principles fixed, different executors (LLM judge versus majority vote) agree only $73\\%$ of the time. 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