The players can discuss it to themselves if needed but the easiest answer is for them to post in a collab. That is, they go to a chatroom, PM or a site that provides collab writing service like titanpad and then RP there until they're satisifed about the scene, they needed GM's input/part or the scene's over.

So, yes, you're thinking it wrong, it's not "who should take charge of everyone?" The only one allowed to control other players are GM and its to be used sparingly. It's "Who wants to cooperate a post in this scene?

:btw This sort of question should be in Roleplay Discussion.