Effective leadership in competition

Among natural biological flocks/swarms or even mass social activities, when the collective behaviors of the followers has been dominated by the moving direction or opinion of one leader group, it seems very difficult for later-coming leaders to reverse the orientation of the mass followers, especially when they are in quantitative minority. This Letter reports a counter-intuitive phenomenon, Following the Later-coming Minority, provided that the late-comers obey a favorable distribution pattern which enables them to spread their influence to as many followers as possible in a given time and to accumulate enough power to govern these followers. We introduce a discriminant index to quantify the whole group's orientation under competing leadership, which helps to design an economic way for the minority later-coming leaders to defeat the dominating majority leaders solely by optimizing their distribution pattern. Our investigation provides new insights into the effective leadership in biological systems, with meaningful implication to social and industrial applications.