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Mattis, a fellow Stoic, is the best choice and there is no way the Republican congress doesn't give him the waiver. He's a Marine's Marine and arguably the finest combat leader of our age, although McChrystal might have something to say about that. He's so popular with the rank and file military that they can't really oppose him.
That said, I predict that this appointment will not end well for Trump. Trump values personal loyalty above all but Mattis is loyal to a higher ideal. If he wants someone that will look him in the eye and dress him down when he says or does something stupid, that's Mattis. I don't think Trump will like that any better than Obama did.