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pirate 4 would not ignore them, since he will risk dying if he doesn't comply to their demands. my idea breaks if a pirate prefers death over being alive. he already knows the others might actually be unreasonable (from his viewpoint), so he has to take that into account. the pirates killing one other pirate *might* harm themselves *if* the next proposal is lousy for them, but they also might convince the next pirate to give them a better deal.
to extract the main cracking point:
if a rational player can choose between a 100% chance to get 1 coin and an x% chance to get 50 coins, which is the rational choice? can you even say one is rational and the other isn't? isn't it more like gambling, where you cannot know which choice is better? in this concrete example, acting out of character would make it impossible (at least for me) to predict what all the other pirates might do now, since the domain of the game changed.
if there was only a single round, then no matter what number 5 offers, as long as it is a single coin, those who get a coin should agree to the proposal since 1 > 0.
but here we have more than one round.
the problem i have here is the definition of rational.
if i were pirate number 1-3, i would reject number 5th offer if it was 98-0-1-0-1, thereby showing number 4 that i want to maximize the number if coins i get and that i would be ready to kill him if he does not do what i say. why is this not rational? excluding a pirate from the game increases your own chance to get more coins. showing a pirate that you will kill him if he does not offer what you want is also good for your outcome, so why not do it?
i can see how to reach the 98-0-1-0-1 conclusion, but why stop there? why is "1 coin for sure" more rational than "maybe 50 coins"? why wouldn't it be rational to make an irrational move to change the game and increase your potential win?
does rational mean taking no risk?
i disagree with the official solution.
what keeps the 4 pirates from collaborating and blackmailing the first none into offering 25 coins for everyone and one for himself? how would this be considered irrational?
how is a sure 1 coin more rational than a sure 25 via blackmail?
what keeps any combination of two pirate to sell their votes for 50 coins each?
since not dying is the oldest pirates highest priority, he needs to buy at least 2 votes.
now either he pays 25 coins to each pirate, 50 to two, or they decide to betray him anyway for the chance of repeating the whole process but trying to blackmail more coins out of number 4.
the problem is priorities. will a pirate take 25 coins, or will he risk his life to get more? they are missing in the riddle description.
even if you go the 100% rational route, they could still let the first pirate die and "teach" number two that way that they are not willing to agree to a lousy 1 coin.
here is how it would go
pirates 1-4 say "give me 50 coins and i will vote for you"
pirate 5 either does so and gets 50% of the votes or tries his rationality thing and dies.
next step:
pirates 1-3 say "give me 100 coins and i will vote for you" (or 50 in the other version)
pirate 4 either picks one/two and does as the others want, or he dies.
next step:
same thing happens
next step:
number 2 gives himself 100 coins and wins, or in the other variation, gives 100 to number one.
why wouldn't it happen this way? why would pirates 1+3 accept 1 or 2 coins and not try to get 50/100?
this is a bit like the ultimatum game + being allowed to make statements before the other one makes his offer.
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