A sweeping statement from an old conversation, followed by more sweeping states from myself:
Writers do not decided who their influences are, scholars do, and scholars have to come to a consensus as to how to go about doing that and a consensus as to who influences whom.
This statement is too thin a blanket to be spread so broadly:it's backwards. Writers do decide who their influences are. The act of preferring one writer over another with regard to value , style and impact constitutes a choice, choice being a decision. This personal canon-formation, a nascent writers' set of examples of what writing can be, ought to be, and where writing ought to grow from, is obviously a set of choices, albeit convoluted. Likewise, I doubt that there's a moment in a writer's activity when they are not aware of the shadow of past genius that is cast over them, the Greats--however defined--that they aim their work away from, toward an originality, and maybe genius,that is their own. The anxiety of influence, courtesy of Harold Bloom, is almost an observable dynamic in sensible study.
The scholar, in turn, only uncovers who the influences are in the course of credible research, but does not choose them. The temptation may be great, but the theorist/scholar/critic can speculate only so much in their interpretation of real data. Writers begin with private views and prejudices about the given world, perceived through their eyes, their sets of experience, but an aim of writing to begin with is too seek consensus: it's the shock of recognition, among other things, that gives the aesthetic satisfaction with a narrative that's rendered well. Private projects don't stay private: they enter into the reading world in an attempt to give us more ideas, fixtures, metaphors to help us think about ourselves .
That is all, I think, that literature can ever promise, the work itself. Criticism , like literature proper, is hardly a fixed set of standards, a Biblical claim of absolute, final totality. It's an activity that's adjacent, secondary to, literature, and at best can act as an aid to the reader seeking to underline salient elements that dovetail, enlarge, or illuminate the problematic nature of experience that won't, and cannot, tell you what it means.