 Anonymity: For any admissible profiles \(\langle v_1, v_2 , \ldots ,v_n\rangle\) and \(\langle w_1, w_2 , \ldots ,w_n\rangle\) that are permutations of each other (i.e., one can be obtained from the other by reordering the entries), the social decision is the same, i.e., \(f(v_1, v_2 , \ldots ,v_n) = f(w_1, w_2 , \ldots ,w_n)\).