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8 members have voted

unJon
unJon
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January 17th, 2019 at 5:56:16 AM permalink
Thought Iíd toss out a math question Iíve heard given in interviews.

There are five pirates: captain, first mate, second mate, third mate and fourth mate. The pirates are rational actors and have the following preferences:

1) Pirates prefer to live rather than die.
2) So long as life not in jeopardy, Pirates prefer more gold rather than less.
3) All else being equal, Pirates prefer to make other Pirates walk the plank (killing them) than not.

Pirates follow the strict pirate code for sharing booty. The highest ranking pirate makes a proposal about how to share the booty and then everyone votes. If a majority (more than half) vote in favor of the plan, the booty is shared that way. Otherwise, the pirate that made the proposal has to walk the plank, and the next highest pirate makes a proposal.

The five pirates just made a score of 100 gold pieces.

How will the 100 gold pieces be shared?

Answers in spoilers please.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
Wizard
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Wizard
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January 17th, 2019 at 7:22:59 AM permalink
This is one of my favorite logic puzzles, but I ask it with 1,000 coins and I reorder the priorities as follows:

1) So long as life not in jeopardy, Pirates prefer more gold rather than less.
2) All else being equal, Pirates prefer to make other Pirates walk the plank (killing them) than not.
3) Pirates prefer to live rather than die.

Where this might make a difference is if a pirate is put in a position where he gets no gold either way. Would he give up his own life to have another pirate walk the plank? Under my rules the answer is "yes."

I'll put a 24-hour delay on myself to give the rest of the forum a chance to enjoy it.
It's not whether you win or lose; it's whether or not you had a good bet.
boymimbo
boymimbo
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January 17th, 2019 at 7:42:01 AM permalink
the first and second mate get 50 each.

We assume the first party always votes for the plan. To get then majority the captain needs two more votes. He offers 50 and 50 to the two mates. If either of those two vote against the plan they know the captainis going to die. The first mate prefers life over death and then gold. The only thing the first mate can do is offer the 2nd and third mates 50 each. The second mate knows that if the first mate gets killed then he will get no gold as he will have to offer the third and fourth mates all of the gold. Therefore the 1st and 2nd mates will accept 50 each from the captain and win the vote 3 to 2, and everyone lives. It says everyone votes so i presume it includes the person offering the deal.


Maybe?
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Ayecarumba
Ayecarumba
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January 17th, 2019 at 9:51:44 AM permalink
Quote: unJon

Thought Iíd toss out a math question Iíve heard given in interviews.

There are five pirates: captain, first mate, second mate, third mate and fourth mate. The pirates are rational actors and have the following preferences:

1) Pirates prefer to live rather than die.
2) So long as life not in jeopardy, Pirates prefer more gold rather than less.
3) All else being equal, Pirates prefer to make other Pirates walk the plank (killing them) than not.

Pirates follow the strict pirate code for sharing booty. The highest ranking pirate makes a proposal about how to share the booty and then everyone votes. If a majority (more than half) vote in favor of the plan, the booty is shared that way. Otherwise, the pirate that made the proposal has to walk the plank, and the next highest pirate makes a proposal.

The five pirates just made a score of 100 gold pieces.

How will the 100 gold pieces be shared?

Answers in spoilers please.



My initial guess is that the Captain proposes a three way split. The booty would be divided 32/34/34, with the Captain getting the small share. The first mate and second mate would also get offers. If the First Mate turns on the Capt, he will still have to deal with proposing the same split to three other pirates, who all have an incentive to vote it down. If the Second Mate turns on the Captain, then turns on the First Mate, he will be left making a proposal to two others who have an incentive to vote him down to get a 50/50 share by making him walk the plank. They both can do no better.

What happens if, should it get to four voters, there is a tie? Does the proposer walk the plank?
Simplicity is the ultimate sophistication - Leonardo da Vinci
Wizard
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Wizard
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January 17th, 2019 at 10:46:14 AM permalink
Quote: Ayecarumba

What happens if, should it get to four voters, there is a tie? Does the proposer walk the plank?



Yes. Majority means over 50%.
It's not whether you win or lose; it's whether or not you had a good bet.
gordonm888
gordonm888
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January 17th, 2019 at 1:19:48 PM permalink
I've never heard this one before and I have not looked it up on the internet. Here is my off-the-top-of-my-head answer.



The five pirates are captain, 1st mate, 2nd mate, 3rd mate and 4th mate.

Third mate does not want the decision to slide down to him, because 4th mate will always vote no on his decision, kill the 3rd mate and take all the money.

2nd mate wants the decision to slide down to him, he can propose that 100% of the money go to himself and third mate must vote for it to save his own life. Thus 2nd mate has the potential to win 100% of the loot, leaving 3rd mate and 4th mate with zero.

First mate knows all of the above. If the decision come to him he can keep 98 gold pieces and give 1 each to the 3rd and 4th mates, That's a better deal for 3rd and 4th mate then they would get from 2nd mate, so they would accept this and vote yes to prevent 2nd mate from getting the decision.

Therefore, Captain can split the money 96 for him, 0 for 1st and 2nd mates and 2 each for 3rd and 4th mates. That is the best deal that the 3rd and 4th mates will get, therefore they will vote yes.

Last edited by: gordonm888 on Jan 17, 2019
Sometimes, people are just a bottomless mystery. And, after all, this is just a sh*tty little forum in the sun-less backwaters of the online world.
Ayecarumba
Ayecarumba
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January 17th, 2019 at 4:39:46 PM permalink
Quote: gordonm888

I've never heard this one before and I have not looked it up on the internet. Here is my off-the-top-of-my-head answer.



The five pirates are captain, 1st mate, 2nd mate, 3rd mate and 4th mate.

Third mate does not want the decision to slide down to him, because 4th mate will always vote no on his decision, kill the 3rd mate and take all the money.

2nd mate wants the decision to slide down to him, he can propose that 100% of the money go to himself and third mate must vote for it to save his own life. Thus 2nd mate has the potential to win 100% of the loot, leaving 3rd mate and 4th mate with zero.

First mate knows all of the above. If the decision come to him he can keep 98 gold pieces and give 1 each to the 3rd and 4th mates, That's a better deal for 3rd and 4th mate then they would get from 2nd mate, so they would accept this and vote yes to prevent 2nd mate from getting the decision.

Therefore, Captain can split the money 96 for him, 0 for 1st and 2nd mates and 2 each for 3rd and 4th mates. That is the best deal that the 3rd and 4th mates will get, therefore they will vote yes.



...that's not the best deal for the Fourth Mate. He has a chance to split 50/50 with the third mate, or take it all.
Simplicity is the ultimate sophistication - Leonardo da Vinci
unJon
unJon
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January 17th, 2019 at 5:32:51 PM permalink
Quote: gordonm888

I've never heard this one before and I have not looked it up on the internet. Here is my off-the-top-of-my-head answer.



The five pirates are captain, 1st mate, 2nd mate, 3rd mate and 4th mate.

Third mate does not want the decision to slide down to him, because 4th mate will always vote no on his decision, kill the 3rd mate and take all the money.

2nd mate wants the decision to slide down to him, he can propose that 100% of the money go to himself and third mate must vote for it to save his own life. Thus 2nd mate has the potential to win 100% of the loot, leaving 3rd mate and 4th mate with zero.

First mate knows all of the above. If the decision come to him he can keep 98 gold pieces and give 1 each to the 3rd and 4th mates, That's a better deal for 3rd and 4th mate then they would get from 2nd mate, so they would accept this and vote yes to prevent 2nd mate from getting the decision.

Therefore, Captain can split the money 96 for him, 0 for 1st and 2nd mates and 2 each for 3rd and 4th mates. That is the best deal that the 3rd and 4th mates will get, therefore they will vote yes.

. This is really close!
Error in the last step. Captain can save a gold piece.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
charliepatrick
charliepatrick
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January 17th, 2019 at 11:23:37 PM permalink
Quote: gordonm888

I've never heard this one before and I have not looked it up on the internet. Here is my off-the-top-of-my-head answer.



The five pirates are captain, 1st mate, 2nd mate, 3rd mate and 4th mate.

Third mate does not want the decision to slide down to him, because 4th mate will always vote no on his decision, kill the 3rd mate and take all the money.

2nd mate wants the decision to slide down to him, he can propose that 100% of the money go to himself and third mate must vote for it to save his own life. Thus 2nd mate has the potential to win 100% of the loot, leaving 3rd mate and 4th mate with zero.

First mate knows all of the above. If the decision come to him he can keep 98 gold pieces and give 1 each to the 3rd and 4th mates, That's a better deal for 3rd and 4th mate then they would get from 2nd mate, so they would accept this and vote yes to prevent 2nd mate from getting the decision.

Therefore, Captain can split the money 96 for him, 0 for 1st and 2nd mates and 2 each for 3rd and 4th mates. That is the best deal that the 3rd and 4th mates will get, therefore they will vote yes.



Under the rules that earlier people have to offer strictly more money, for instance if 2nd offers no money to 3rd, wizard's question says they'd rather die and kill off another pirate if they're going to get no money. Thus the figures for each round have to be larger than those on offer later.
3rd mate knows if it gets to him he gets no money as 4th will vote against him.
2nd mate has to offer 3rd mate some money (this is where wizard's rule starts to change things) so 2nd can keep 99 and offer 1 to 3rd mate to get his vote.
1st mate now has to offer more to 3rd and 4th to get their votes, so keeps 97 and gives 2 to 3rd and 1 to 4th.
Similarly captain has to offer even more, so 3 to 3rd and 2 to 4th, so can only keep 95.

If the rules were as originally stated 2nd mate wouldn't have to offer any money (as 3rd would prefer to live). However the captain still has to offer 2 to 3rd and 4th (to beat the later offer) so keeps 96.
Ayecarumba
Ayecarumba
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January 18th, 2019 at 8:58:15 AM permalink
Quote: charliepatrick

Quote: gordonm888

I've never heard this one before and I have not looked it up on the internet. Here is my off-the-top-of-my-head answer.



The five pirates are captain, 1st mate, 2nd mate, 3rd mate and 4th mate.

Third mate does not want the decision to slide down to him, because 4th mate will always vote no on his decision, kill the 3rd mate and take all the money.

2nd mate wants the decision to slide down to him, he can propose that 100% of the money go to himself and third mate must vote for it to save his own life. Thus 2nd mate has the potential to win 100% of the loot, leaving 3rd mate and 4th mate with zero.

First mate knows all of the above. If the decision come to him he can keep 98 gold pieces and give 1 each to the 3rd and 4th mates, That's a better deal for 3rd and 4th mate then they would get from 2nd mate, so they would accept this and vote yes to prevent 2nd mate from getting the decision.

Therefore, Captain can split the money 96 for him, 0 for 1st and 2nd mates and 2 each for 3rd and 4th mates. That is the best deal that the 3rd and 4th mates will get, therefore they will vote yes.



Under the rules that earlier people have to offer strictly more money, for instance if 2nd offers no money to 3rd, wizard's question says they'd rather die and kill off another pirate if they're going to get no money. Thus the figures for each round have to be larger than those on offer later.
3rd mate knows if it gets to him he gets no money as 4th will vote against him.
2nd mate has to offer 3rd mate some money (this is where wizard's rule starts to change things) so 2nd can keep 99 and offer 1 to 3rd mate to get his vote.
1st mate now has to offer more to 3rd and 4th to get their votes, so keeps 97 and gives 2 to 3rd and 1 to 4th.
Similarly captain has to offer even more, so 3 to 3rd and 2 to 4th, so can only keep 95.

If the rules were as originally stated 2nd mate wouldn't have to offer any money (as 3rd would prefer to live). However the captain still has to offer 2 to 3rd and 4th (to beat the later offer) so keeps 96.



Doesn't he turn down all offers since he actually has a chance to kill everyone else and keep 100% for himself? Why would he accept 2 when he can have 100?
Simplicity is the ultimate sophistication - Leonardo da Vinci

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