 Preference aggregation rules are normally expected to produce orderings as their outputs, but sometimes we may only require partial orderings or not fully transitive binary relations. An aggregation rule that produces transitive but often incomplete social preferences is the Pareto dominance rule: here, for any profile \(\langle R_1, R_2 , \ldots ,R_n\rangle\) and any \(x, y \in X\), \(xRy\) if and only if, for all \(i \in N\), \(xP_i y\). An aggregation rule that produces complete but often intransitive social preferences is the Pareto extension rule: here, for any profile \(\langle R_1, R_2 , \ldots ,R_n\rangle\) and any \(x, y \in X\), \(xRy\) if and only if it is not the case that, for all \(i \in N\), \(yP_i x\). Both rules have a unanimitarian spirit, giving each individual veto power either against the presence of a weak social preference for \(x\) over \(y\) or against its absence.