Hmm... good question. Do we want to treat the GM like an ordinary cabinet officer, or give this post some Constitutional scaffolding?
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Personally, I think it requires some constitutional guarantee, even a minimal one. Otherwise, there's nothing that prevents not having a Game Engine or Game Moderator and we don't have an impartial figure to simulate results (and without that one might argue many things would be pointless in excercise). On the other hand, the least thing we need is to extend debate too much and it is a matter a future Congress should be able to discuss in more detail.
May I suggest an amendment in which we establish that the Republic of Atlasia will have a "Game Engine" to determine current and future events, simulate the consecuences of actions and legislation, and provide necessary information to the game? That means there's Constitutional standing for the future, but it leaves it open to Congress to debate whether to have a GM or several, what powers it will have, and so on.
While not a delegate, I believe something simple like this would do: