DrPizza
Administrator Elite Member Goat Whisperer
Well, you're just so-so logical. I guess it's pretty logical to sit around pouting that you didn't get any coins, rather than to get 1 coin.
This is a Catch-22
If all other 4 pirates are extremely greedy, then they know all they have to do is disagree and, you, as the senior are taken out of the running (meaning the money recycles itself to 4 people instead of 5). This process can repeat itself until there is only the youngest pirate left, or until the majority of the pirates are satisfied enough to not keep 100%.
But assuming that each pirate is looking to get all the money, the only thing you can do is bow out of the running as the senior pirate, tell them that the money is divided among the younger 4 pirates in whatever way they see fit. That is the only way to survive, although you get 0%. But chances are you would die and get 0% anyways.
If we assume that you can reason with the 2nd and 3rd in line, and explain to them that this is the only way for them to keep up to 1/3 of the money, you can then proceed to haggle, but given the premise, this cannot be done.
PowerEngineer
Diamond Member
- Oct 22, 2001
- 3,615
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Well, I'll take a shot at it. Let's not get too critical...
If there's just one pirate, obviously he gets 100 coins.
If there are two pirates, the most senior proposes 100 coins for himself and 0 for the less senior. Since the senior votes will vote yes, he's assured at least 50% of the vote and gets the coins and his life.
Note that the least senior is therefore guaranteed to get zero if it comes down to just two pirates. If he's logical, he knows his only chance at any coins is to make a deal while there are still more than two pirates.
If there are three pirates, then the most senior knows that the "middle senior" will always vote against him (since if the number drops to two, he gets 100 guaranteed). He also knows that anything other than zero is a step up for the least senior. Therefore, he should offer 1 coin to the least senior, none to the "middle senior", and keep 99 coins for himself. If logic prevails, he should get two votes "yes".
Note that the second least senior pirate should now see that he will be skunked if the number gets down to three, so he must make a deal before then too.
If there are four pirates, then the most senior should be able to offer 1 coin to either of the two least senior pirates and keep 99 coins for himself (and give zero to the other two). He should still get two "yes" votes, which is enough to prevail.
Now the third least senior pirate has the same revelation. If the number of pirates drops to four, he will get zip too.
Finally now, with five pirates, the most senior pirate should be able to offer 1 coin to any two of the three least senior pirates and keep 98 coins for himself. He should get three "yes" votes and prevail.
Sorry... Didn't see others had already arrived at this solution!
If there's just one pirate, obviously he gets 100 coins.
If there are two pirates, the most senior proposes 100 coins for himself and 0 for the less senior. Since the senior votes will vote yes, he's assured at least 50% of the vote and gets the coins and his life.
Note that the least senior is therefore guaranteed to get zero if it comes down to just two pirates. If he's logical, he knows his only chance at any coins is to make a deal while there are still more than two pirates.
If there are three pirates, then the most senior knows that the "middle senior" will always vote against him (since if the number drops to two, he gets 100 guaranteed). He also knows that anything other than zero is a step up for the least senior. Therefore, he should offer 1 coin to the least senior, none to the "middle senior", and keep 99 coins for himself. If logic prevails, he should get two votes "yes".
Note that the second least senior pirate should now see that he will be skunked if the number gets down to three, so he must make a deal before then too.
If there are four pirates, then the most senior should be able to offer 1 coin to either of the two least senior pirates and keep 99 coins for himself (and give zero to the other two). He should still get two "yes" votes, which is enough to prevail.
Now the third least senior pirate has the same revelation. If the number of pirates drops to four, he will get zip too.
Finally now, with five pirates, the most senior pirate should be able to offer 1 coin to any two of the three least senior pirates and keep 98 coins for himself. He should get three "yes" votes and prevail.
Sorry... Didn't see others had already arrived at this solution!
DrPizza
Administrator Elite Member Goat Whisperer
*sigh* And if they're extremely logical as well as greedy, 2 of those 4 pirates realize that they aren't going to get a single coin if the first pirate is gone. It's a majority vote, not a unanimous vote. Pirate 1 only needs to offer them 1 coin each; at that point it becomes 1 or nothing for 2 of the pirates.
The unfortunate part of this problem is it applies to the real world as well... presidential candidates dwell on appeasing only a few select states (i.e. Florida.) Which presidential candidate really cares about Wyoming's electoral votes?
YOyoYOhowsDAjello
Moderator<br>A/V & Home Theater<br>Elite member
- Aug 6, 2001
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But you wouldn't get another shot. Pirate 2 would be greedy and give himself 99 and Pirate 4 one coin. You would get nothing.
Your options are 1 coin or 0 coins.
Of course this means Pirate #1 is dead because he made a bad offer. And Pirate #2 is about to meet the same fate for the same reason.
Pirate #4 is just as greedy as #5 and doesn't want just one coin. He thinks the same as me, #5, and expects to receive at least the nominally fair value of 20 gold pieces. In fact all 5 pirates should feel that any proposal that offers less than 20 gold pieces mean death for the pirate offering such a plan.
The 'nominally fair value' for is 20 gold pieces per pirate. Because they're all greedy they'll opt for any division plan that provides a reasonable chance of them getting more than 20 gold pieces. They should not vote "yes" for any plan that has 100% certainty of getting less than 20 gold pieces.
They vote for the distribution scheme that matches their greed and tolerance for risk. Nobody dies.
If the original question excluded death and was re-worded that pirate #1 was just out of the running for the 100 gold, then yes, the whole crap-ola 1 gp might fly.
YOyoYOhowsDAjello
Moderator<br>A/V & Home Theater<br>Elite member
- Aug 6, 2001
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You don't have to start bolding stuff
I understand that the "fair" option would be to have everyone get 20 coins, but who is going to vote for that? The answer is 3, 4, and 5 would all love to get that deal since Pirate 2 is going to be very greedy and offer 1 gold to pirate #4. You can be generous and offer 20 gold to all of them, but Pirate 2 is going to vote no since if it goes one more round, he can manage to get 99. Pirate 3 will be offered nothing the next round as will 5. Pirate 4 would be offered 1 unless Pirate 2 was not greedy (but he is).
3 and 5 would vote yes since they'd get nothing the next round. 20 is better than nothing. 1 is also better than nothing and would be my offer since I am greedy.
You get 4's vote (which you dont' really need) since he will not get nearly as good an offer from greedy #2 in the next round.
Anyway...
Pirate 1 is not dead because #3 and #5 voted "YES" since the alternative is they will get nothing.
Zero gold and Death is the worst outcome for all these pirates.
Zero gold and Live is the second worst outcome
Some gold and Live is what they all want
I'm offering "Some gold and Live" to a couple of pirates that are either going to end up with "Zero gold and Live"
You can make other offers that get more than the two votes you need, but this maximizes the amount of money you will get.
Would you agree that if it came down to two pirates, #4 would say 100 for me, 0 for you?
(who would then vote for himself and win?) <-- maximum profit for himself, he wants to get to this point.
Would you agree that if it came down to three pirates, #3 would say 99 for me, and 1 for #5?
#3 gives one gold to #5 since #5 knows that in the next round, he'll get nothing from #4.
Getting some gold and living is better than getting zero gold and living. Since #3 is greedy, he offers the lowest amount greater than #5 so that this offer is better than going to the next round. So, he offers one gold. <-- maximum profit for #3, he wants to get to this point.
Would you agree that if it came down to four pirates, #2 would say 99 for me, and 1 for #4?
#4 knows that if it goes one more round, he's not getting any of the gold. His options are vote now and get one gold, or vote no to the 1 gold offer and get no gold at all.
Now we come to the original problem. In this situation we know that if it goes one more round, #2 is going to be at maximum profit, so he wants the deal to go through. Due to the previous reasons, #4 is going to vote yes in the next round as long as he gets more than zero gold from #2's offer.
#3 and #5 are going to get screwed the next round and get nothing when #2 and #4 vote yes.
Their choice is vote "No" and get zero gold and live or I can offer them some gold and live as their option in my deal. Since I'm greedy, I'll offer them one each.
YOyoYOhowsDAjello
Moderator<br>A/V & Home Theater<br>Elite member
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SSSnail
Lifer
- Nov 29, 2006
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There are no logical answers to this stupid riddle, only theoretical answers as none of the answers could ever account for human greed or individual logic. If I was pirate, I'd want everything, so if I'm given less than anything of a fair share, I'd vote NO.
I've seen this somewhere before, and very recently too.
GrantMeThePower
Platinum Member
- Jun 10, 2005
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I don't know if the answer has been posted yet, becasue i didn't want to ruin it, but this is what i would do (just after reading the OP).
Assume for a moment that it comes down to the last two-anything less than a 100 percent to the lowest pirate would have him vote against the 2nd senior, hence killing him and keeping 100%.
But the first pirate couldn't say give 100% to the last pirate because then the other 3 would vote against it and he would die.
So, he has to make each one get just enough to keep them happy.
You also have to assume automatically that the last pirate will veto the proposal no matter what. THat means that you have 3 pirates left who make the deciison (assuming the first pirate always votes for his own idea, that cancels out the last pirate who, no matter what, will vote against it). So out of those 3 pirates, two of them need to agree to it.
So lets say that you give 0 percent to the last two pirates, knowing that no matter what they will veto what you proposed. You then have to make it worthwhile to the last two pirates.
If they kill you, how much would they get? Assuming your proposal is denied, then the next pirate would need 2 of the other 3 pirates to agree, meaning he could give the last pirate 0, splitting the winnings 3 ways.
If his gets denied, then the 3rd pirate would only need to get one other to agree with him.
Now, we know that the fourth pirate already can't do anything to win. The third pirate, then, giving him anything other than zero would make him have to accept it or face death. So the 4th place pirate gets 1%.
The third place pirate is then in a position where if he votes against pirates one and two, then he would get 99% of the loot. But if pirate number 4 gets even 2%, then he would replace pirate 3's vote for pirate four, and pirate four could just pay the last pirate 1%, leaveing pirate number 3 with zero.
The second place pirate, knowing this, could then pay the 3rd place pirate even 1%, the fourth place pirate could get the other pirate votes by giving number 4 3% and number 5 2% and keeping 94%.
Returning to the first pirate: He can accept two pirates voting against him. So he ignores the second place pirate, who could get 94% by pirate number 1 losing and pirate number 4, who would recieve at least 3% if pirate 1 loses. Pirate 3 and pirate 5 are the ones, then, that he needs to appease. Pirate 5 could get 2% (knowing he wouldn't get any more than that even if pirate 1 loses), and pirate 3 could get 1%, matching his greatest possible total if pirate 1 loses. That leaves pirate 1 with 97%. No one would be happy, but he would get the required 2 votes. (of course, you may want to bump those up 1% to give them a 'better' deal than if he loses, leaving him with 95%)
EDIT-OOPS! I thought the op said you needed MORE than 1/2, not just 1/2. The end result would be the same, but you have to switch between pirate 4 and 5.
Assume for a moment that it comes down to the last two-anything less than a 100 percent to the lowest pirate would have him vote against the 2nd senior, hence killing him and keeping 100%.
But the first pirate couldn't say give 100% to the last pirate because then the other 3 would vote against it and he would die.
So, he has to make each one get just enough to keep them happy.
You also have to assume automatically that the last pirate will veto the proposal no matter what. THat means that you have 3 pirates left who make the deciison (assuming the first pirate always votes for his own idea, that cancels out the last pirate who, no matter what, will vote against it). So out of those 3 pirates, two of them need to agree to it.
So lets say that you give 0 percent to the last two pirates, knowing that no matter what they will veto what you proposed. You then have to make it worthwhile to the last two pirates.
If they kill you, how much would they get? Assuming your proposal is denied, then the next pirate would need 2 of the other 3 pirates to agree, meaning he could give the last pirate 0, splitting the winnings 3 ways.
If his gets denied, then the 3rd pirate would only need to get one other to agree with him.
Now, we know that the fourth pirate already can't do anything to win. The third pirate, then, giving him anything other than zero would make him have to accept it or face death. So the 4th place pirate gets 1%.
The third place pirate is then in a position where if he votes against pirates one and two, then he would get 99% of the loot. But if pirate number 4 gets even 2%, then he would replace pirate 3's vote for pirate four, and pirate four could just pay the last pirate 1%, leaveing pirate number 3 with zero.
The second place pirate, knowing this, could then pay the 3rd place pirate even 1%, the fourth place pirate could get the other pirate votes by giving number 4 3% and number 5 2% and keeping 94%.
Returning to the first pirate: He can accept two pirates voting against him. So he ignores the second place pirate, who could get 94% by pirate number 1 losing and pirate number 4, who would recieve at least 3% if pirate 1 loses. Pirate 3 and pirate 5 are the ones, then, that he needs to appease. Pirate 5 could get 2% (knowing he wouldn't get any more than that even if pirate 1 loses), and pirate 3 could get 1%, matching his greatest possible total if pirate 1 loses. That leaves pirate 1 with 97%. No one would be happy, but he would get the required 2 votes. (of course, you may want to bump those up 1% to give them a 'better' deal than if he loses, leaving him with 95%)
EDIT-OOPS! I thought the op said you needed MORE than 1/2, not just 1/2. The end result would be the same, but you have to switch between pirate 4 and 5.
GrantMeThePower
Platinum Member
- Jun 10, 2005
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Ok, another, easier to read version:
Start from the end:
2 pirates left, pirate 4 gets all of it
3 pirates left-pirate 5 needs only 1% to make it worth his while (because otherwise he gets zero) pirate 3 gets 99%
4 pirates left- pirate 5 needs 1% to match, pirate 4 needs only 1% to be better than with 3 pirates left, so pirate 2 keeps 98%
5 pirates left- pirate 5 needs 1%, pirate 4 needs 1%. If he wants to bump them up he can and still win.
Start from the end:
2 pirates left, pirate 4 gets all of it
3 pirates left-pirate 5 needs only 1% to make it worth his while (because otherwise he gets zero) pirate 3 gets 99%
4 pirates left- pirate 5 needs 1% to match, pirate 4 needs only 1% to be better than with 3 pirates left, so pirate 2 keeps 98%
5 pirates left- pirate 5 needs 1%, pirate 4 needs 1%. If he wants to bump them up he can and still win.
YOyoYOhowsDAjello
Moderator<br>A/V & Home Theater<br>Elite member
- Aug 6, 2001
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Pirate 2 only needs one more vote, so he can do
99 for himself
1 for the cheapest one to buy off (pirate 4)
If it goes one more round, Pirate 2 gets 99, Pirate 4 gets 1.
That means 3 and 5 will get nothing, so you can buy them each off with 1.
That's why I think you pay 3 and 5, not 4 and 5.
Nope. It would be insanity, as Albert Einstein would say, for Pirate #3 to make the same offer as the late Pirates #1 and #2 and expect a different result.
The fatal flaw in the 98-1-1 solution is that it ignores the death penalty. That solution wrongly suggests that the pirates are more fearful of getting squat than they are fearful of dying. (If the death sentence was omitted then pirates who's proposal were voted down would still live, and thus that solution might apply.) A gold-less Pirate #5 would still be ahead of the gold-less and deceased Pirates # 1, #2, and #3.
Pirates at the head of the queue should not think, 'what minimum offer can I make that's better then the offer of the pirate after me'. Instead he should ask, 'what offer maximizes my chances of both staying alive and getting gold'.
A pirate who offers 1 gold piece is essentially saying, 'I can give you more that 1 gold piece but I'm only offering you 1 as my life is worth only 1 gold piece. Kill me if you want more'. He's betting his life that the greedy pirates who hold his life in their hands will be satisfied with the 1 gold piece offer.
More gold may come but death is forever.
---
If Pirates #3, #4, and #5 would like the fair plan, perhaps #1 should offer it.
---
Will Pirate #5 vote for death if only offered 1 gold piece? Will he for spite, knowing he'll get squat vote death? Is getting only 1 gold all that valuable to him?
The answer is for him to tell the other pirates what is he willing to settle for in exchange not to vote for a death sentence. He does this by selecting a distribution plan from A-G. If all pirates are equally greedy they'll pick the same or similar plans. Picking from A-G is essentially a form of negotiation without a long debate. Then they draw their straws, take their chances, and no blood is dropped.
Nope. It would be insanity, as Albert Einstein would say, for Pirate #3 to make the same offer as the late Pirates #1 and #2 and expect a different result.
The fatal flaw in the 98-1-1 solution is that it ignores the death penalty. That solution wrongly suggests that the pirates are more fearful of getting squat than they are fearful of dying. (If the death sentence was omitted then pirates who's proposal were voted down would still live, and thus that solution might apply.) A gold-less Pirate #5 would still be ahead of the gold-less and deceased Pirates # 1, #2, and #3.
Pirates at the head of the queue should not think, 'what minimum offer can I make that's better then the offer of the pirate after me'. Instead he should ask, 'what offer maximizes my chances of both staying alive and getting gold'.
A pirate who offers 1 gold piece is essentially saying, 'I can give you more that 1 gold piece but I'm only offering you 1 as my life is worth only 1 gold piece. Kill me if you want more'. He's betting his life that the greedy pirates who hold his life in their hands will be satisfied with the 1 gold piece offer.
More gold may come but death is forever.
---
If Pirates #3, #4, and #5 would like the fair plan, perhaps #1 should offer it.
---
Will Pirate #5 vote for death if only offered 1 gold piece? Will he for spite, knowing he'll get squat vote death? Is getting only 1 gold all that valuable to him?
The answer is for him to tell the other pirates what is he willing to settle for in exchange not to vote for a death sentence. He does this by selecting a distribution plan from A-G. If all pirates are equally greedy they'll pick the same or similar plans. Picking from A-G is essentially a form of negotiation without a long debate. Then they draw their straws, take their chances, and no blood is dropped.
YOyoYOhowsDAjello
Moderator<br>A/V & Home Theater<br>Elite member
- Aug 6, 2001
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Yes, I understand that there are two elements that are in play here, life/death and gold/nothing, but my answer is the ony one that seems logical to me.
If we think that a pirate will not pick
"1 gold piece and live" over "0 gold pieces and live" because of spite, then I don't think there is an answer.
I think I have the "correct answer" to this logic puzzle. You are saying it would be more complicated because a pirate would put more value on his life and want to give himself the maximum chance of being saved. If that is the case, is there an answer? We would have to offer two pirates more than they would have gotten as their maximum amount to satisfy their greed.
I think the whole problem is rather goofy so whatever
If we think that a pirate will not pick
"1 gold piece and live" over "0 gold pieces and live" because of spite, then I don't think there is an answer.
I think I have the "correct answer" to this logic puzzle. You are saying it would be more complicated because a pirate would put more value on his life and want to give himself the maximum chance of being saved. If that is the case, is there an answer? We would have to offer two pirates more than they would have gotten as their maximum amount to satisfy their greed.
I think the whole problem is rather goofy so whatever
Kyteland
Diamond Member
- Dec 30, 2002
- 5,747
- 1
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No, if you ignored the death penalty they would propose 100-0-0-0-0. 3 and 5 are going to get 0 anyway if it moves to the next round, so they might as well vote yes from the get-go to screw over 2 and 4. You're #1 for a reason, right?
Since this was clearly stated as a logic problem, you can't use psychological arguments like "If I was only offered 1 I would vote no even though there was a chance I would get 0 on the next round." In the framework of pure logic the correct answer is 98-0-1-0-1.
If you want a psychological experiment, try this one on.
You are isolated in a room with another (arbitrary) person isolated in another room. There is $100 at stake. You must make this person an offer on how to split that $100 between yourselves. If they decline your offer you both get nothing, but if they accept you both get your money determined by your offer. You don't get to talk to them, only have an intermediary bring your (purely numerical) offer to them. There's no negotiation. You don't know anything about this person or what they would be willing to accept. What do you offer?
Your answer to this question is basically how risk adverse you are. I personally would offer them $10, but most people tend to offer closer to $50.
That is incorrect.
98-1-1 is the minumun offer to stave off an automatic no vote from all other pirates. However, that offer is not the same as an acceptable offer. If the death penalty is removed, 98-1-1 might apply because noone dies.
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