At the end of the day, a GM is always an entertainer, and the players are the people being entertained. Though unlike other media, the players are not only audience but active participants.There's a goodly amount of meat to talk about in considering what authority is given, by whom, and what are the limits of that authority.
But there's another thing that, eventually, probably ought to be discussed - what are the responsibilities that come with the authority?
I know we like to think of the situation in which we have been given power of some scope, and within that scope, we get to do whatever we want. But as a practical matter, is that the way things function? If you aren't fulfilling your responsibilities, your freedom to act in whatever way you choose is pretty much inconsequential, isn't it?
A GM does have power, but the purpose of the power is the enjoyment of the players. GMs who want players to dance to their tune to act out some kind of play that they want to see of course exist, but that's universally considered "doing it wrong" by anyone discussing this subject. Even GMs defending such behavior excuse it as being necessary to create more fun for the players.
GMs have a "natural authority" simply by the functions they perform that players don't even have to consciously give to them. GMs generally organize the game, prepare the game, and usually provide most of the game material. This automatically or instinctively establishes that the GM is in charge. Even in games played at the place of one of the players, or when a player is put in charge of the scheduling, the game is not "on" unless the GM says so. Players can be late, excuse themselves from the play space, or tell the others to start playing without them while they'll finish up their character sheet. When the GM stops, the game stops. Players can discuss among themselves what they want to do next, but those are discussions about what they will do once the game resumes. If the GM doesn't hear it, it wasn't played.
And this holds true for all RPGs that have a GM.
The questions which moves/actions/declarations can be made by either the GM or the players is subject to the rules of the specific game system. There can be a great range of authorizations that the rules grant to GMs and players. But the metagame authority described above exist outside the game system and simply follow from natural human group dynamics.
I think the most extreme form of maximum player autonomy and minimal GM authority would be found in player versus player wargames with a neutral referee. A term that can be found in various retroclones and presumably some really old D&D editions, even though it is no longer appropriate. The referee in a wargame can simply stand aside and let the players play by themselves, only making judgement calls about the implementation of the rules when the players are in disagreement, but not deciding a single thing of what happens in the game.