 The first three conditions are analogous to universal domain, ordering, and anonymity in preference aggregation. The last is the counterpart of independence of irrelevant alternatives, though stronger: it requires that (i) the collective judgment on any proposition \(p \in X\) (of which a binary ranking proposition such as ‘\(x\) is preferable to \(y\)’ is a special case) depend only on individual propositions on \(p\) (the independence part), and (ii) the pattern of dependence between individual and collective judgments be the same across all propositions in \(X\) (the neutrality part). Formally, independence is the special case with quantification restricted to \(p = q\). Propositionwise majority voting satisfies all these conditions, except the consistency part of collective rationality.