Theorem 1: monotonic caution
If every component score is coordinatewise nondecreasing, adding or increasing a recognized risk feature cannot produce a less cautious recommendation.
For states x and x-prime where x-prime is at least as risky on every recognized coordinate, each component score is greater than or equal to its previous value. Their sum S(x-prime) is therefore greater than or equal to S(x). Ordered thresholds preserve that ordering, so the protocol cannot move to a less cautious band.