@Major: I think one of the weaknesses of Diplomacy as a game is that the goal isn't a bit more clearly defined, at least in the original ruleset. It's designed as a zero-sum game, but if different players have different goals, the game doesn't work so well.
On webDiplomacy, this problem is solved by using an explicit scoring system. So, in a PPSC game, the goal is to acquire the most centers possible at the time the game ends, and in a WTA game, the goal is to get 18 centers, or, failing that, be part of the fewest-player draw you can get.
Maybe that's actually a better way to think about the problem with multi-gaming. Diplomacy, like almost all games, is intended to be played such that the goals for every player are known and are in conflict with each other. When you allow outside influences to alter your goal, that's no longer true, and so the game doesn't really work as intended.
The "diceman" idea has a similar problem. Do I like drawing Austria in a gunboat game? No, I don't. But I signed up for a game implicitly promising that I'd do my best to win, and knowing that 1/7 of the time I would be asked to play Austria. The other players deserve to play against an Austria doing its best to win, even if my best as Austria is often ineffective. To go back to the pickup game analogy, this is like agreeing to play a game, choosing teams, and then deciding that because the three best players ended up on the other team, you're just going to sit down on the court and let the others play 4 on 5 until it ends. Would you be invited back to play again?
Basically, if you're playing against me, I want you to bring your 'A' game, and I want to find out whether I'm good enough to take your best shot and win anyway (knowing that no matter how good I am, I'm going to lose more than I win in a seven-player game). I don't think you'd be proud of a victory against six "dicemen", right? I think it's only fair to you that if you win, you can feel that you've won something, and I ask the same in return.