Another interesting thought is that there are some (very tightly structured) roleplaying games that do away with a separate referee entirely.
As I understand it, Nixon's Dunjon does this, as does one whose precise name escapes me (
but LostSoul is wise and kind: Polaris) (it won an award of some sort fairly recently), in which each player has a position to play at the table, and represents an aspect of each of several interlinked characters (All I remember is that you're supposed to light a candle before each game, and drink chilled white wine and listen to Sigur Ròs whilst playing. I never said it was an unpretentious game!).
In other words, the Fog of War effect that seems to require a narrator can, with proper protocols, be sustained by players alone.
It's just tricky. Imagine, for instance, if each player ran two characters; their own character, and the nemesis of another. By having a larger number of game sessions, or structuring each session appropriately, you could prevent any character from learning the plans of his nemesis.
Alternatively, each player could represent the nemesis of another, and for each action a player attempts, be responsible for ensuring that the outcome matches the observed facts of the scene thus far, and have some sort of bidding system to ensure commensurate penalty to apparent risk.
(actually, that sounds kind of interesting. Maybe I should write this up.)
If any action required the votes of the non-involved players to determine success/failure/unexpected ramifications, the narrator role has been sufficiently spread around.
I probably wouldn't play this game too often, since it involves a LOT more structure than I'm used to, but there's no
one narrator character, and is fairly tightly structured, more so than I usually enjoy.
It might be fun to play this before getting into a game to reflect the struggles of the gods while creating the world, though, leading to a shared campaign that has something interesting to each of the players.
It's also definitely not D&D
PS: Oo, my brain tingles from the interesting conversation. Thanks, Reynard!