The Confidence Gate Theorem: When Should Ranked Decision Systems Abstain?

ArXi:2603.09947v1 Announce Type: new Ranked decision systems -- recommenders, ad auctions, clinical triage queues -- must decide when to intervene in ranked outputs and when to abstain. We study when confidence-based abstention monotonically improves decision quality, and when it fails. The formal conditions are simple: rank-alignment and no inversion zones. The substantive contribution is identifying why these conditions hold or fail: the distinction between structural uncertainty (missing data, e.g., cold-start) and contextual uncertainty (missing context, e.g., temporal drift.