 Independence of irrelevant alternatives: For any two profiles \(\langle R_1, R_2 , \ldots ,R_n\rangle\) and \(\langle R^*_1, R^*_2,\ldots, R^*_n\rangle\) in the domain of \(F\) and any \(x, y \in X\), if for all \(i \in N\), \(R_i\)’s ranking between \(x\) and \(y\) coincides with \(R^*_i\)’s ranking between \(x\) and \(y\), then \(xRy\) if and only if \(xR^*y.\)