When he gets to asserting the "sole" function is this negotiation, that's philosophy.
RPGing involves the creation of shared fiction; that's the main thing that distinguishes it from a boardgame.You put it in quotes, so you obviously know you just subbed in a term that made this a strawman. Why do this?
RPGs are about shared fiction, and how that fiction is created is a negotiation. We use game systems to operationalize and codify these negotiations with mechanics, but that doesn't really change that what's happening is a discussion and negotiation about what we're going to all pretend together.
Because the fiction is shared, there needs to be a means of establishing agreement about its content. This is what Vincent Baker calls negotiation - the process whereby a group of humans reaches agreement. If anyone prefers another word for that process, I don't think it's a big deal. The point is that, for RPGing to work, the participants need to reach agreement in respect of the content of the shared fiction. Vincent Baker summarises that as negotiated imagination.
@hawkeyefan gave some clear and simple examples upthread: by declaring that my PC attacks the Orc, I am putting it up for grabs that the shared fiction includes an Orc defeated by my PC in combat. How do we decide if the fiction actually changes in that way? Different systems have different answers, but a widely-shared one is to invoke combat resolution mechanics.
EDIT: I think the tangent in which @S'mon, @prabe and @Ovinomancer discuss whether processes of reaching agreement by deferring to authority count as negotiations or not is largely unproductive. The key point that Vincent Baker is making is that agreement has to be reached, and that this is what game mechanics facilitate.
I think there is probably a second, more sub-textual point, which is that in the context of RPGing whatever authority there is is granted quite immediately by the participants and can be revoked largely at will - which is a marked difference from (say) a judicial tribunal and some arbitral tribunals. But that seems orthogonal to a discussion about the relationship between player experience and (imagined) character experience.
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