 Independence of irrelevant alternatives: For any two profiles \(\langle W_1, W_2 , \ldots ,W_n\rangle\) and \(\langle W^*_1, W^*_2,\ldots, W^*_n\rangle\) in the domain of \(F\) and any \(x, y \in X\), if for all \(i \in N\) \(W_i(x) = W^*_i(x)\) and \(W_i (y) = W^*_i(y)\), then \(xRy\) if and only if \(xR^*y\).