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So if 9 says to 7, "Give me $999 or I'm voting against you," wouldn't a rational 7 give it to 9 rather than dying to spite 9?

9 *wouldn't* say that to 7, because 9 knows that if he says this, and #7 refuses, then 7 dies and 9 gets nothing. 9 will not spite himself; he knows that it's rational to only expect 1 and that he is liable to get nothing if he tries for anything more. Again, he's not playing the lottery here; he's not going to pass up a small payoff for a "chance" at a bigger payoff, because HE KNOWS THAT ALL THE OTHER PLAYERS ARE RATIONAL. He can deduce what everyone else must be thinking.

You're not comparing apples to apples when you're trying to measure leverage.
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