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I'm saying your hypothetical is outside the bounds of the problem.All of the pirates are rational and make their decisions (what to offer, vote yes or no) without needing to communicate with the other players.If it is rational for 9 to vote against 7, he will do so.The problem is set up so that if at any time a player who is getting money (or who is not getting money but gets a chance to survive where he previously didn't have one) as a result of a deal, votes against the deal, if the other players are rational, the "defector" gets zilch (or killed).7 doesn't "accept" or "refuse"; he just makes an offer.Greater amounts are preferable to lesser amounts, but it is irrational to let your desire for a greater amount lead you vote in such a way as you could get zero.
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