 One much-discussed class of aggregation rules violating independence consists of the premise-based rules. Here, a subset \(Y \subseteq X\) of logically independent propositions (and their negations) is designated as a set of premises, as in the court example. For any profile \(\langle J_1, J_2 , \ldots ,J_n\rangle , J = \{p \in X : J_Y\) entails \(p\}\) where \(J_Y\) are the majority-accepted propositions among the premises, formally \(\{p \in Y : |\{i \in N : p \in J_i\}| \gt n/2\}\). Informally, majority votes are taken on the premises, and the collective judgments on all other propositions are determined by logical implication. If the premises constitute a logical basis for the entire agenda, a premise-based rule guarantees consistent and (absent ties) complete collective judgment sets. (For a more general definition, see Dietrich and Mongin 2010. The procedural and epistemic properties of premise-based rules are discussed, e.g., in Pettit 2001; Chapman 2002; Bovens and Rabinowicz 2006; Dietrich 2006.)