Ambiguity in pirates problem.
I got a little side-tracked in the pirate puzzle, because I had never heard of a system where one could vote on the proposal he himself made! Once I read teh beginning of the solution, I reworked it and got the proper result.
Just to add clarification: a pirate wants to make sure he'll live, so his offer must be BETTER for his voters than if he were killed off. He is not going to just match the amount and hope they are merciful.
This is the same as requiring a strict majority of the pirates to agree on the issue, assuming that a pirate will always vote for his own scheme, which is the way I first interpreted this (though I see now that I got it wrong). Well, you'd solve this in exactly the same way as the others:
Having thought about these pirates a bit more (lovely problem, eh?) I'm not sure that we're being sufficiently piratical in our thinking. What happens if a pirate refuses to abide by the rules? Presumably the other pirates will kill him for trying to cheat them. But pirate 2 in the above scenario knows that this is going to happen anyway, so his best strategy from both a survival and a monetary point of view is to murder pirate 1 while pirate 1 is waiting for him to come up with a suggestion. Of course, pirate 1 knows this, so if it gets down to the two of them there's just going to be a fight. Now, what does this do to pirate 3's strategy ...?
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