 Given consistent individual judgment sets, unanimity rule guarantees consistent collective judgment sets, because the intersection of several consistent sets of propositions is always consistent. Supermajority rules guarantee consistent collective judgment sets too, provided the quota \(q\) is chosen to be at least \((k-1)/k\), where \(k\) is the size of the largest minimal inconsistent subset of \(X\) (Dietrich and List 2007a). The reason is combinatorial: any \(k\) distinct supermajorities of the relevant size will always have at least one individual in common. So, for any minimal inconsistent set of propositions (which is at most of size \(k)\) to be supermajority-accepted, at least one individual would have to accept all the propositions in the set, contradicting this individual’s consistency. Conclusion-based rules, finally, produce consistent collective judgment sets by construction, but always leave non-conclusions undecided.