I think that for any statement that the GM is not the final arbitrator of events within the game to be true, even with what you're calling Gygaxian play, you have to be relying on a definition of arbitrate that is so nuanced that it is functionally useless.
I don't agree. Here's an illustration (borrowed in general outline from Ronald Dworkin's well known essay on "The Model of Rules").
In an election, citizens cast votes. The electoral official then count the votes and declare the outcome. In some tolerable sense of "arbitrate" the electoral officials are the final arbiters of the outcome of the vote. But it would be wildly misleading to suggest that this means that they, rather than the voters, have subtantive responsibility for deciding the outcome of the election. They are mere procedural gatekeepers.
If your candidate loses, it makes no sense in this situation to complain to the electoral officials. Go out and remonstrate with your fellow citizens!
Now consider the Florida count in the Bush vs Gore presidential election. In determining whether or not the Florida count was violating Bush's 14th Amendment rights. Whatever one's theory of constitutional decision-making, it's hard to argue that there is a mechanical resolution of the legal question that was before the court. The Supreme Court were therefore the final arbiters of the outcome of that election in a far more substantive sense.
In this sort of case, if your candidate loses it makes perfect sense to remonstrate with the Supreme Court.
Now consider an election in Stalin's Soviet Union. Stalin is the final arbiter of the outcome of that election in an entirely straightforward way - he just makes up the result! If your candidate loses, I'm sorry but that means you took political action against Stalin and are on your way to a gulag.
Is the role of the GM in Gygaxian play closer to that of the electoral officials, closer to that of the Supreme Court, or closer to that of Stalin? I think it's mostly like the role of the electoral officials - a type of procedural role - and occasionally like that of the Supreme Court - an interpretive and robustly adjudicative role. It should never be like Stalin.
Of course the GM is the final arbitrator of events within the game.
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To assert that the GM is not the final arbiter strikes me as either a fundamental misunderstanding or an attempt to bamboozle the reader about what is going on in favor of some polemical position.
Well, to me, asserting that "of course the GM is the final arbitrator of events within the game", without considering the range of other ways the game can be and has been played, strikes me as projection of one's own approach onto the game in general.
I have one player, in particular, whose expectations for play seem to have been shaped by playing with a GM like [MENTION=17106]Ahnehnois[/MENTION] who (judging from the exchange above with [MENTION=22779]Hussar[/MENTION]) requires GM approval of any deployment of resources or abilites by a player (eg a player in Ahehnois's game cannot initiate a Diplomacy action without GM authorisation). That player always asks me, "Can I make a Diplomacy check?" or "Can I make a Perception check?". Whereas my expectation is that, once I've framed the situation, it is the players who simply declare what it is that their PCs are doing. Hence they decide, in those moments of play, what events are happening in the game. They don't need my permission to change or contribute to the fiction.