Rerankers, reward models and multi-document QA scorers score candidate documents or responses in one LLM prompt, so each score depends on their order. Such scorers are selected on ranking quality, but their scores determine a decision: what a score threshold retains, a reader answers, or a preference model selects. However, equal ranking quality does not imply equal decisions: on passage reranking, five trained scorers within 0.010 nDCG@10 retain sets that overlap by only 0.66-0.84 when reordered. A published reranker takes the highest retained-set F1 in our comparison and still overlaps by only 0.667. No prompt-time change we test removes that order dependence: the only one that gains ranking quality leaves all three decisions unchanged. Order-consistency SFT (OC-SFT) attenuates it in the weights, training a candidate's score not to depend on the order. It holds ranking quality and leads every decision-stability measure among trained scorers on all three tasks: it flips the reader's answer on 0.125 of permutation pairs against 0.149-0.164 for three other objectives that target order. It is more stable than order-averaged distillation on 12 base models, and one OC-SFT permutation retains sets that overlap more than ten averaged off-the-shelf permutations. A comparison should therefore report what a threshold retains and a reader answers, not ranking quality alone. Code is available at https://github.com/thomsonreuters/presentation-dependence.

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