The hidden variables of leadership.

The dynamics of a collective move can be untangled into three components: initiation, following and cancellation. Varying the response function parameters attached to one individual can switch the collective phenomenology from an absence of well identified leader ("distributed leadership") to the emergence of a "despotic regime", i.e. this individual leading more often the collective moves. I show that not all parameters have the same impact but rather that only a large increase of the initiation rate can empower an obvious leader, up to the "despotic" regime. Being more readily followed, or cancelling less often can enhance the leader's prominence only up to a limited level. To overtake this limit would then further require to affect also the parameters attached to the others (e.g. to lower their eagerness to initiate group motion as well as their probability to be followed when they do).