Let's see how smart you are...

[dkgojackets]

If you already know the answer, please don't post immediately and give people a chance to figure it out.

Andrew, Bill, Charles, Dean and Earl are five pirates who have just found 100 gold coins. They now have to divide the loot between them. They have settled on the following bargaining procedure: The pirates go in alphabetical order, starting with Andrew. Each pirate in turn proposes a division of the coins. All pirates vote. If it is accepted by a strict majority, then the coins are divided up and the game is over. If not, the proposer is thrown overboard and eaten by sharks, and then the game is played among the remaining pirates. What should Andrew propose?

To avoid strange answers and technicalities, every pirate wants to maximize their gold. Also, each pirate does not want to die. All pirates will make the optimal decision/vote such that their gold is maxed. All pirates think logically and know the other pirates think logically. "Strict majority" means it must be a majority vote to pass, not a tie. Pirates are not trustworthy, so there is no "deal-making," such as "Vote no and Ill give you X pieces the next round."

[LetsGoPitt]

Re: Let's see how smart you are...

Hmm...this is pretty tough, but let me take a crack at it:

Andrew basically needs to get two of the five pirates on board with his idea to get a majority. So what if two pirates disagree with him, so long as two others agree.

Earl can be completely counted out, since he's the last to propose an idea, and hence will simply say no to everything, hoping everyone else dies so that he's left with all the money.

Dean is probably going to vote down Andrew and Bill's ideas, because all he has to do is say yes to Charles, and he'll get a good chunk of the loot, since he has no chance of getting Earl to approve of his idea and thus would have a tie (and be killed).

Charles can figure on getting at least half of the loot. If he votes down Andrew and Bill (as he knows Dean and Earl will), they'll be killed, leaving just three. Then he can simply split the pot with Dean and beat out Earl's protests 2-1.

Bill is in a tough situation, and is probably going to have to settle for Andrew's idea. He'd like to be able to kill Andrew and split the pot three ways with Charles and Dean, but he knows that Charles wants half of the pot. This would leave the other half to split with Dean. Since Dean is going to hold out for all of the loot, he's certainly not going to OK a 25% share (he needs two more "yes" votes to get the majority).

Andrew, keeping all of this in mind, would probably have to sacrifice some of his money to stay alive. If I were in his place, I would propose giving 50% to Charles to get his vote (since that's what he'll be holding out for), and dividing the other 50% equally with Bill, since 25% is the best Bill could hope for, and he won't get it once Dean's vote matters.

Thus:

Andrew - 25 coins
Bill - 25 coins
Charles - 50 coins
Dean - 0 coins
Earl - 0 coins

[dkgojackets]

Re: Let's see how smart you are...

Some good thoughts, but no.

[Peji911]

Re: Let's see how smart you are...

Pirate 1:0
Pirate 2:0
Pirate 3:0
Pirate 4:0
Pirate 5:100

??

[dkgojackets]

Re: Let's see how smart you are...

Pirate 1:0
Pirate 2:0
Pirate 3:0
Pirate 4:0
Pirate 5:100

??

Very incorrect.

[Peji911]

Re: Let's see how smart you are...

Very incorrect.

haha, thought it was a trick ques

[Beantown]

Re: Let's see how smart you are...

(by alphabetical)
1: 30
2: 25
3: 5
4: 10
5: 35

[dkgojackets]

Re: Let's see how smart you are...

(by alphabetical)
1: 30
2: 25
3: 5
4: 10
5: 35

nadda

[dkgojackets]

Re: Let's see how smart you are...

Hint: work backwards.

[Dallasin2K3]

Re: Let's see how smart you are...

Hmm...this is pretty tough, but let me take a crack at it:

Andrew basically needs to get two of the five pirates on board with his idea to get a majority. So what if two pirates disagree with him, so long as two others agree.

Earl can be completely counted out, since he's the last to propose an idea, and hence will simply say no to everything, hoping everyone else dies so that he's left with all the money.

Dean is probably going to vote down Andrew and Bill's ideas, because all he has to do is say yes to Charles, and he'll get a good chunk of the loot, since he has no chance of getting Earl to approve of his idea and thus would have a tie (and be killed).

Charles can figure on getting at least half of the loot. If he votes down Andrew and Bill (as he knows Dean and Earl will), they'll be killed, leaving just three. Then he can simply split the pot with Dean and beat out Earl's protests 2-1.

Bill is in a tough situation, and is probably going to have to settle for Andrew's idea. He'd like to be able to kill Andrew and split the pot three ways with Charles and Dean, but he knows that Charles wants half of the pot. This would leave the other half to split with Dean. Since Dean is going to hold out for all of the loot, he's certainly not going to OK a 25% share (he needs two more "yes" votes to get the majority).

Andrew, keeping all of this in mind, would probably have to sacrifice some of his money to stay alive. If I were in his place, I would propose giving 50% to Charles to get his vote (since that's what he'll be holding out for), and dividing the other 50% equally with Bill, since 25% is the best Bill could hope for, and he won't get it once Dean's vote matters.

Thus:

Andrew - 25 coins
Bill - 25 coins
Charles - 50 coins
Dean - 0 coins
Earl - 0 coins

I think you're on the right track, but it seems as though Earl's vote would be the cheapest to get. You mention that if the initial ideas are shot down, Charles and Dean will split 50/50, and by default, Earl will be left with nothing.

Thus, Earl's vote should *theoretically* be bought with 1 coin, because that's more than he'll get if the voting gets past Andrew.

Bill's vote should still be available, as per your logic, for 25 coins. That would leave Andrew's proposal at:

Andrew - 74 coins
Bill - 25 coins
Charles - 0 coins
Dean - 0 coins
Earl - 1 coin

Earl would vote for it because nothing is better than something, and that should give it the 3 votes needed. Just a guess.

[dkgojackets]

Re: Let's see how smart you are...

Remember we arent just finding ones that pass, but we are looking for Andrew's optimal proposal here.

[Dallasin2K3]

Re: Let's see how smart you are...

Remember we arent just finding ones that pass, but we are looking for Andrew's optimal proposal here.

In that case.. looking at it again, perhaps Bill's vote may be available for 1 coin also:

If Bill votes no to any proposal by Andrew.. the proposal gets to Bill, who needs three of four votes out of the remaining crew and can't get Charles' or Dean's no matter what he proposes (unless he were to vote yes to a 0/50/50/0 proposal that would leave him with nothing and give Charles and Dean the 50% that they can get by voting Bill down)..

Andrew: 98 coins
Bill: 1 coin
Charles: 0 coins
Dean: 0 coins
Earl: 1 coin

[dkgojackets]

Re: Let's see how smart you are...

the proposal gets to Bill, who needs three of four votes out of the remaining crew and can't get Charles' or Dean's no matter what he proposes

But does he need both of theirs?

[Dallasin2K3]

Re: Let's see how smart you are...

But does he need both of theirs?

Ah, this is true. I think I've got it but we'll let someone else jump in now. Good one.

[dkgojackets]

Re: Let's see how smart you are...

PM me to satisfy your curiosity.