Outcome-Neutral Promotion Through Hierarchical Consistency Gates: Sensitivity, Bias Flow Across Layers, and Fairness-Suppression Tradeoffs

Selection and certification pipelines often promote draft outcomes to records only after passing local consistency tests (e.g. redundancy checks, anomaly vetoes, committee-style screening). Rather than relying on post-hoc propensity fitting or downstream fairness constraints, we analyze the gate mechanism directly. We model promotion as a Boolean gate applied to binary inconsistency flags and show that the promoted distribution is exactly the draft distribution conditioned on promotion: P(i | G = 1) = P piai j pjaj , ai := P(G = 1 | i), so all macroscopic distortion is mediated by outcome-dependence of the promotion weights. We derive exact sensitivity laws for threshold gates under i.i.d. Bernoulli checks, obtaining the exact derivative identity a ′ (q) = −m m−1 τ q τ (1 − q) m−1−τ , yielding explicit Lipschitz and log-sensitivity bounds and showing that strict vetoing (τ = 0) amplifies residual check asymmetry linearly in m. For without-replacement (hypergeometric) checks we prove an exact one-step discrete derivative for tail probabilities, linking redundancy parameters to the propagation of outcomedependent dissent. In the two-outcome case we derive an additive log-odds recursion across layers, making bias flow through deep hierarchies explicit. Monte Carlo sweeps validate the exact identities and separate true certification distortion from sampling mismatch, including rare-event regimes where empirical total variation is noise-dominated. The results are portable across gate families and check models (iid and without-replacement) and apply to multistage screening and record-promotion procedures beyond any single fairness doctrine. Scope: we quantify selection-induced distortion and tradeoffs; we do not propose a normative fairness definition, do not claim optimal gate design, and do not assert causal or legal fairness guarantees.