 Technically, the growing-reliability conclusion follows via a non-trivial combinatorial argument. The infallibility conclusion has an easy proof, which can be sketched here. By UC, general competence \(p=P(R_{i})\) is voter-independent. The group’s proportion of correct votes is a random variable that converges stochastically to \(p\) by the law of large numbers, using UI. So, as \(p&gt;\frac{1}{2}\) by UC, the probability that this proportion exceeds \(\frac{1}{2}\), which is precisely \(P(\Maj_{n})\), converges to 1 as \(n\rightarrow\infty\).