proposition. Finite audit-gate bound [ftip-00EF]
proposition. Finite audit-gate bound [ftip-00EF]
Let \(N\in \mathbb N_{\geq 1}\) and \(0\leq \eta \leq 1\). Assume these \(N\) candidates are audited and each invalid candidate is falsely accepted with marginal probability at most \(\eta \). Then the probability that some invalid candidate is accepted is at most \(N\eta \), by the union bound of Lemma [ftip-00E6]. This conclusion does not require independence.
The statement bounds existence of an accepted invalid candidate. A selected output guarantee additionally requires a typed selection rule and its relation to the audit decisions.