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D'oh got it wrong again.
If we say they all do not like throwing pirates overboard then C can still propose 100,0,0 as D will not get any gold either way and we now know he doesn't like throwing other pirates overboard.
So we get to A being able to propose 97,0,1,2,0 or 97,0,1,0,2 whether the rule is pirates like throwing other pirates overboard or do not like it.
However, if we are not sure whether pirates like throwing other pirates overboard and in particular C does not know whether D would want to throw C overboard if the gold coin distribution is the same then it is safer for C to offer D a gold coin and the proposed solution given of 97,0,1,0,2 is correct.
5 pirates is a nice problem,
http://www.mathsisfun.com/puzzles/5-pirates.html
but as you increase the number of pirates, the patterns get intricate and worth seeing.
First a couple of additional rules, because otherwise the solutions are not unique:
Only whole number of gold coin solutions can be proposed and they don't trust any other agreement.
If a pirate can bribe two or more different pirates for the same number of gold coins and doesn't need to bribe them all then he prefers to bribe the highest ranking pirate.
My answer
Let me know if you do not agree.
First we need a rule of whether pirates like to throw other pirates overboard if it makes no difference to the gold they get.
If we say they like throwing pirates overboard then:
If it gets to D making a proposal, he is doomed as E can vote against to get all the gold and enjoy throwing D overboard.
Therefore C can propose 100,0,0 and D will vote for the proposal in order to survive. With 1 vote each this goes through.
B can propose 98,0,1,1 and get the 2 votes needed
So A can propose 97,0,1,2,0 or 97,0,1,0,2
If we say they do not like throwing pirates overboard then it works as the proposed solution 97 0 1 0 2
JacobCrofts, if there is only E left he will take the gold with no one left to vote or disagree. He is going to believe 0 votes out of 0 fulfils the 50% requirement - half of 0 votes is zero votes required (even if not initially convinced of that, an alternative of committing suicide is unsurprisingly remarkably persuasive to most people). Plus there is no-one to argue or try to throw him overboard. Therefore it works as the proposed solution or if pirates enjoy throwing pirates overboard then as I suggest.
>"Because Eddie(youngest) will anyway have a second chance to earn at least 1 coin when its Colin's (middle) turn."
That is more wishful thinking than rational logic. If A proposal does not get enough votes, B will make a proposal B 99, C 0, D 1, E 0 and that will be voted through because D won't be offered any by C. D prefers 1 to 0 so votes with B giving the two votes needed for that distribution to be agreed. Therefore, C will not get to have a turn at making a proposal. So if C or E vote down A's proposal of 98,0,1,0,1 then they will get nothing. Therefore it makes sense for them to vote to accept 1 gold coin.
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