Communities and groups often need to make decisions grounded by social norms and preferences, such as when moderating content or providing judgments for aligning AI systems. Prevailing approaches to provide this grounding have primarily centered around constructing high-level guidelines and criteria, similar to legal ``constitutions''. However, it can be challenging to specify social norms and preferences consistently and accurately through constitutions alone. In this work, we take inspiration from legal systems and introduce ``case law grounding'' (CLG) -- a novel approach for grounding decision-making that uses past cases and decisions (precedents) to ground future decisions in a way that can be utilized by human-led processes or implemented through prompting large language models (LLMs). We evaluate how accurately CLG grounds decisions with five groups and communities spread across two decision task domains, comparing against a traditional constitutional grounding approach, and find that in 4 out of 5 groups, decisions produced with CLG were significantly more accurately aligned to ground truth: 16.0--23.3 %-points higher accuracy using the human-led process, and 20.8--32.9 %-points higher when prompting LLMs. We also evaluate the impact of different configurations of CLG, such as the case retrieval window size and whether to enforce binding decisions based on selected precedents, showing support for using binding decisions and preferring larger retrieval windows. Finally, we discuss the limitations of our case-based approach as well as how it may be best used to augment existing constitutional approaches when it comes to aligning human and AI decisions.
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