 The paradigmatic example of a preference aggregation rule is pairwise majority voting, as discussed by Condorcet. Here, for any profile \(\langle R_1, R_2 , \ldots ,R_n\rangle\) and any \(x, y \in X\), \(xRy\) if and only if at least as many individuals have \(xR_i y\) as have \(yR_i x\), formally \(|\{i \in N : xR_i y\}| \ge |\{i \in N : yR_i x\}|.\) As we have seen, this does not guarantee transitive social  preferences.[5]