This is interesting. Suppose the players want to play a traditional style game. They want to explore the world and have it revealed to them by the DM as they go. They want to explore dungeons that they didn't help bring into being. And so on. Wouldn't getting into a game like that give them a lot of say over what the game is about since it chases what the players are interested in?
It seems to me that a traditional player in a game of
@pemerton's style would have little say and it would not chase what that player is interested in, just like traditional play doesn't give Pemerton what he is interested in giving him little say in a game of that style.
Similar to the above, if the player wants to play in a traditional style game, then he is getting his say by having the PC knowledge figured out in traditional manner.
Same as above.
It seems to me that it really is one thing, Playstyle preference. If you are playing a game that runs the style of your preference, you have a lot of say. If you are playing a game that is of the other playstyle, then you don't have a lot of say.