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.