 Positive responsiveness: For any admissible profile \(\langle v_1, v_2 , \ldots ,v_n\rangle\), if some voters change their votes in favour of one alternative (say the first) and all other votes remain the same, the social decision does not change in the opposite direction; if the social decision was a tie prior to the change, the tie is broken in the direction of the change, i.e., if [\(w_i \gt v_i\) for some \(i\) and \(w_j = v_j\) for all other \(j\)] and \(f(v_1, v_2 , \ldots ,v_n) = 0\) or 1, then \(f(w_1, w_2 , \ldots ,w_n) = 1\).