I think some incredibly interesting points were brought into the light by the intersection of
@Charlaquin and
@Thomas Shey
Because when I first read Charlaquin's example of the player pulling out a key that never existed, and the rest of the table agreeing with them, I laughed. Because, in my experience, the rest of the table is either silent (and expecting the DM to handle confronting someone, because they are mostly people who do not want a confrontation) or they are telling the other player to shut up and stop trying to cheat.
And, like Thomas said, if you are making a ruling, and 4 out of 6 players disagree with your ruling... that's a problem. But, if you make a ruling and 5 out of 6 players agree with you... you almost didn't need to make a ruling at all.
And this is the part of the debate that gets twisted all around on itself. These arguments and debates usually focus on 1 DM and 1 player. And in that scenario, it is a 50/50 split of opinion. Except, it often then comes up that "My players all enjoy my games" or "I've been running for the same group for years and they all agree with me" or some other way to indicate that the "
real" situation is the DM and five players against a single player, making it a 84/16 split in opinion, favoring the DM. Which obviously is a very different scenario.
That makes these discussions so difficult though, because you are either in a true 50/50 split, or you are assuming that the majority of the table is agreeing with you.
But how many DMs here would actually overrule a majority of their players? If you wanted to run a campaign about being in the Roman Republic, and 5/6's of your players said no, would you run the game? No. You've been overruled.
If you say that the stealth rules work X, but 5/6's of your players say it is Y, do we really think that the DM is going to insist on overruling their table, or do we think there is going to be a discussion as they try and convince the rest of the table to agree with them?
I think this is why the idea that the DM is actually the ultimate authority is losing traction. Because the authority the DM is deriving is from the rest of the table agreeing with them. If the table disagrees with them, then the authority vanishes.