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Résumé : We study how instruction-tuned LLMs arbitrate direct conflicts between system and user instructions. We introduce a benchmark of 41 paired constraints with deterministic verifiers and evaluate eight models under matched baseline, conflict, and same-channel control conditions. Behaviourally, the models split into three regimes by System Authority Delta: hierarchy-respecting models use the system channel as an authority signal, anti-hierarchy models follow the system less often than their same-channel baseline predicts, and no-effect models show little channel sensitivity. Llama-3.1-8B is the strongest anti-hierarchy case in our suite, following the system in only 0.10 of conflict trials. We use this behavioural failure case to ask whether user-preferring arbitration reflects the absence of an internal conflictresolution signal. It does not: on Llama-3.1-8B, the conflict outcome is linearly decodable from residual-stream activations at 0.97 balanced accuracy, 17 percentage points above a metadata-only baseline, with analogous signals on Qwen2.5-7B and gpt-oss-20b. Steering with a layer-12 mean of four per-conflict logistic-regression directions raises genuine system compliance from 0.132 to 0.530, while directions selected mainly for pooled separability steer poorly. User-preferring conflict resolution can therefore coexist with a readable internal arbitration signal, and successful intervention depends on the geometry of the readout rather than probe accuracy alone