In the case of a tie, the proposer holds the casting vote to break the tie. The next strongest pirate takes over and then offers a split of the money. The process is repeated until a proposal is accepted. How does the game play out? MindYourDecisions now has over 1, free articles with no ads thanks to community support!
Help out and get early access to posts with a pledge on Patreon. The YouTube channel EckoChamb3r offers a careful and detailed explanation of how to find the solution. Start at the end of the game. What would happen if the game continued so only pirate E remained? This is a trivial case as pirate E would take all coins for himself. Now reason backwards one step. What would happen if the game got to pirate D proposing a split? Similarly, pirate D would take all coins for himself.
While pirate E would oppose the split, pirate D is in favor, so the vote would be tied at Pirate D could then cast the tie-breaking vote and make the proposal go through. Now comes the interesting part when we reason one more step backwards.
What would happen if pirate C is offering the split? Pirate C needs to buy 1 vote to make the plan go through. If pirate C dies, then pirate D would take all coins and pirate E ends up with nothing. All the pirates know this. This presents an opportunity to buy the vote of pirate E. Pirate C does not take all coins for himself. Instead pirate C offers 1 coin to pirate E.
Each of the living pirates votes on the proposal, and if half or more of the pirates vote yes, then the proposal is accepted, the treasure is shared according to those terms, and the process is over.
If the proposal does not receive enough votes, then the pirate who proposed it is made to walk the plank and dies, at which point the pirate next in authority makes a new proposal, to be voted on in the same way.
Because the pirates are all rational, intelligent, and greedy, each will think carefully about how to maximize gold for himself. Because they are all murderous, each pirate would prefer to murder one or more of his fellows, as long as it does not reduce his own share of gold. You are pirate A, the first pirate to make a proposal.
If only pirates D and E are still living, then D is in an excellent position. Help out and get early access to posts with a pledge on Patreon. Start at the end of the game. What would happen if the game continued so only pirate E remained? This is a trivial case as pirate E would take all coins for himself. Now reason backwards one step. What would happen if the game got to pirate D proposing a split? Similarly, pirate D would take all coins for himself.
While pirate E would oppose the split, pirate D is in favor, so the vote would be tied at Pirate D could then cast the tie-breaking vote and make the proposal go through. Now comes the interesting part when we reason one more step backwards. What would happen if pirate C is offering the split?
Pirate C needs to buy 1 vote to make the plan go through. If pirate C dies, then pirate D would take all coins and pirate E ends up with nothing. All the pirates know this.
This presents an opportunity to buy the vote of pirate E. Pirate C does not take all coins for himself. Instead pirate C offers 1 coin to pirate E. Now pirate E can either vote for this split and get 1 coin, or pirate E can vote against it which leads to getting nothing when pirate D is in charge.
So pirate E prefers this plan and would vote for it. What would happen if pirate B was in charge? Pirate B similarly needs to buy 1 vote. The easiest vote to buy is pirate D, who ends up with nothing if the split fails and pirate C ends up in charge.
Now we return to the original situation. What does pirate A do? Pirate A needs to buy two votes in order to make a proposal pass. Pirate C is a likely candidate because he ends up with nothing if pirate A dies. This means pirate C has a vested interest in keeping pirate A alive. If pirate A gives him any reasonable offer—in theoretical sense, even a single gold coin—pirate C would accept the plan.
Pirate A will offer 1 gold coin to pirate C, nothing to pirate B, and take 99 coins for himself. The plan will be accepted by pirates A and C, and it will pass.
Amazingly, pirate A ends up with tremendous power despite having two opponents. Luckily, the opponents dislike each other and one can be bought off. The game illustrates the spoils can go to the strongest pirate or the one that gets to act first, if the remaining members have conflicting interests. The leader has the means to buy off weak members. In the real world, it might be necessary to buy a vote with 20 gold coins.
Nonetheless, the general logic is the same. Here are some of the main insights from the game:. I actually strongly disagree with the sentiment that A holds the most power—I think the inverse is true. A is trying to bargain for his life. We take it for granted and assume that the pirates value gold more than their lives, which isn't true.
Pirate A values his life more than his gold. Pirate C should know this. Any settlement less than gold to Pirate B will fail. Using this kind of logic, Pirate A will fail to live unless if he can appease Pirate C, so he -must- appease Pirate C. Then the question of Pirate C's sell-out point is brought into play.
How much is enough? Because we can't discern how much is enough, it becomes a broken example. Not true, Jason H. Pirate C's top priority is getting the most possible coins. Pirate A knows that if he thrown overboard, Pirate C will get nothing.
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