I see 1 rational pirate and 4 utter morons who have paid so much attention to math that they forgot to actually win. I mean, if they were “less rational”, they’d be inclined to get outraged over the unfairness, and throw A overboard, right? And A would expect it, so he’d give them a better deal. “Rational” is not “walking away with less money”.
It’s still an interesting example and thank you for posting it.
I see 1 rational pirate and 4 utter morons who have paid so much attention to math that they forgot to actually win.
Remember, this isn’t any old pirate crew. This is a crew with a particular set of rules that gives different pirates different powers. There’s no “hang the rules!” here, and since it’s an artificial problem there’s an artificial solution.
D has the power to walk away with all of the gold, and A, B, and C dead. He has no incentive to agree to anything less, because if enough votes fail he’ll be in the best possible position. This determines E’s default result, which is what he makes decisions based off of. Building out the game tree helps here.
If B, C, D, and E throw A overboard then C, D, and E are in a position to throw B overboard and any argument B, C, D, and E can come up with for throwing A overboard is just as strong an argument as C, D, and E can come up with for throwing B overboard. In fact, with fewer pirates an even split would be even more advantageous to C, D, and E. So B will always vote for A’s split out of self-preservation. If C throws A overboard he will end up in the same situation as B was originally; needing to support the highest ranking pirate to avoid being the next one up for going overboard. Since the second in command will always vote for the first in command out of self preservation he or she will accept a split with zero coins for themselves. Therefore A only has to offer C 1 coin to get C’s vote. A, B, and C’s majority rules.
In real life I imagine the pirate who is best at up-to-5-way fights is left with 100 coins. If the other pirates were truly rational then they would never have boarded a pirate ship with a pirate who is better at an up-to-5-way fight than them.
If the other pirates were truly rational then they would never have boarded a pirate ship with a pirate who is better at an up-to-5-way fight than them.
When someone asks me how I would get out of a particularly sticky situation, I often fight the urge to glibly respond, by not getting it to said situation.
I digress, if the other pirates were truly rational then they would never let anyone know how good they were at an up-to-X-way fight.
By extension, should truly rational entities never let anyone know how rational they are?
No, they should sometimes not let people know that. Sometimes it is an advantage—either by allowing cooperation that would not otherwise have been possible or demonstrating superior power and so allow options for dominance.
In real life I imagine the pirate who is best at up-to-5-way fights is left with 100 coins.
I doubt it. Humans almost never just have an all in winner takes all fight. The most charismatic pirate will end up with the greatest share, while the others end up with lesser shares depending on what it takes for the leader to maintain alliances. (Estimated and observed physical prowess is one component of said charisma in the circumstance).
I see 1 rational pirate and 4 utter morons who have paid so much attention to math that they forgot to actually win. I mean, if they were “less rational”, they’d be inclined to get outraged over the unfairness, and throw A overboard, right? And A would expect it, so he’d give them a better deal. “Rational” is not “walking away with less money”.
Well if they chose to decline A’s proposal for whatever reason, that would put C and E in a worse position than if they didn’t.
Outrage over being treated unfairly doesn’t come into one time prisoner’s dilemmata. Each pirate wants to survive with the maximum amount of gold, and C and E would get nothing if they didn’t vote for A’s proposal.
Hence, if C and E were outraged as you suggest, and voted against A’s proposal, they would walk away with even less. One gold coin buys you infinitely more blackjack and hookers than zero gold coins.
If C and E—and I’d say all 4 of them really, at least regarding a 98 0 1 0 1 solution—were inclined to be outraged as I suggest, and A knew this, they would walk away with more money. For me, that trumps any possible math and logic you could put forward.
And just in case A is stupid:
“But look, C and E, this is the optimal solution, if you don’t listen to me you’ll get less gold!”
“Nice try, smartass. Overboard you go.”
B watched on, starting to sweat...
EDIT: Ooops, I notice that I missed the fact that B doesn’t need to sweat since he just needs D. Still, my main point isn’t about B, but A.
Also I wanna make it 100% clear: I don’t claim that the proof is incorrect, given all the assumptions of the problem, including the ones about how the agents work. I’m just not impressed with the agents, with their ability to achieve their goals. Leave A unchanged and toss in 4 reasonably bright real humans as B C D E, at least some of them will leave with more money.
...because it’s very hot in Pirate Island’s shark-infested Pirate Bay, not out of any fear or distress at an outcome that put her in a better position than she had occupied before.
Whereas A had to build an outright majority to get his plan approved, B just had to convince one other pirate. D was the natural choice, both from a strict logico-mathematical view, and because D had just watched C and E team up to throw their former captain overboard. It wasn’t that they were against betraying their superiors for a slice of the treasure, it was that the slice wasn’t big enough! D wasn’t very bright—B knew from sharing a schooner with him these last few months—but team CE had been so obliging as to slice a big branch off D’s decision tree. What was left was a stump. D could take her offer of 1 coin, or be left to the mercy of the outrageously blood-thirsty team CE.
C and E watched on, dreaming of all the wonderful things they could do with their 0 coins.
[I think the “rationality = winning” story holds here (in the case where A’s proposal passes, not in this weird counterfactual cul-de-sac) but in a more subtle way. The 98 0 1 0 1 solution basically gives a value of the ranks, i.e., how much a pirate should be willing to pay to get into that rank at the time treasure will be divided. From this perspective, being A is highly valuable, and A should have been willing to pay, say, 43 coins for his ship, 2 coins for powder, 7 coins for wages to B, C, D, E, etc., to make it into that position. C, on the other hand, might turn down a promotion to second-in-command over B, unless it’s paired with a wage hike of one 1 coin; B would be surprisingly happy to be given such a demotion, if her pay remained unchanged. All the pirates can win even in a 98 0 1 0 1 solution, if they knew such a treasure would be found and planned accordingly.]
It seems to me that the extent to which B C D E will be able to get more money is to some extent dependent on their ability to plausibly precommit to rejecting an “unfair” deal… and possibly their ability to plausibly precommit to accepting a “fair” one.
Emphasis on “plausibly” and “PIRATES.”
At minimum, if they can plausibly precommit to things, I’d expect at the very least CDE to precommit to tossing A B overboard no matter what is offered and splitting the pot three ways. There are quite possibly better commitments to make even than this.
Heh, if I can’t convince you with “any possible math and logic”, let me try with this great video (also that one) that shows the consequences of “reasoning via outrage”.
Watched the first one. It was very different from the scenario we’re discussing. No one’s life was at stake. Also the shares were unequal from the start, so there was no fair scenario being denied, to get outraged about.
I’m not in favor of “reasoning via outrage” in general. I’m simply in favor of possessing a (known) inclination to turn down overly skewed deals (like humans generally have, usefully I might add); if I have it, and your life is at stake, you’d have to be suicidal to propose a 98 0 1 0 1 if I’m one of the people whose vote you need.
What makes it different from the video example is that, in the pirate example, if I turn down the deal the proponent loses far, far more than I do. Not just 98 coins to my 1, but their life, which should be many orders of magnitude more precious. So there’s clearly room for a more fair deal. The woman in that case wasn’t like my proposed E or C, she was like a significantly stupider version of A, wanting an unfairly good deal in a situation when there was no reason for her to believe her commitment could reliably prevail over the other players’ ability to do the same.
Watched the first one. It was very different from the scenario we’re discussing. No one’s life was at stake. Also the shares were unequal from the start, so there was no fair scenario being denied, to get outraged about.
A suggestion to randomize was made and denied. They fail at thinking. Especially Jo, who kept trying to convince herself and others that she didn’t care about money. Sour grapes—really pathetic.
Whenever I come across highly counterintuitive claims along these lines, I code them up and see how they perform over many iterations.
This is a lot trickier to do in this case compared to, say, the Monty Hall problem, but if you restricted it just to cases in which Pirate A retained 98 of the coins, you could demonstrate whether the [98, 0, 1, 0, 1] distribution was stable or not.
Also, I’d suggest thinking about this in a slightly different way to the way you’re thinking about it. The only pirate in the scenario who doesn’t have to worry about dying is pirate E, who can make any demands he likes from pirate D. What distribution would he suggest?
Edit: Rereading the wording of the scenario, pirate E can’t make any demands he likes from pirate D, and pirate D himself also doesn’t need to worry about dying.
Heh, if I can’t convince you with “any possible math and logic”, let me try with this great video (also that one) that shows the consequences of “reasoning via outrage”.
That shows one aspect of the consequences of reasoning via outrage. It doesn’t indicate that the strategy itself is bad. In a similar way the consequences of randomizing and defending Podunk 1⁄11 times is that 1⁄11 times (against a good player) you will end up on youtube losing Metropolis.
“I will stand firm on A until A becomes worth less than C is now, then I will accept B or C. You get more by accepting B or C now than you get by trying to get more.”
One rational course of action is to mutually commit to a random split, and follow through. What’s the rational course of action to respond to someone who makes that threat and is believed to follow through on it? If it is known that the other two participants are rational, why isn’t making a threat of that nature rational?
I see 1 rational pirate and 4 utter morons who have paid so much attention to math that they forgot to actually win. I mean, if they were “less rational”, they’d be inclined to get outraged over the unfairness, and throw A overboard, right? And A would expect it, so he’d give them a better deal. “Rational” is not “walking away with less money”.
It’s still an interesting example and thank you for posting it.
Remember, this isn’t any old pirate crew. This is a crew with a particular set of rules that gives different pirates different powers. There’s no “hang the rules!” here, and since it’s an artificial problem there’s an artificial solution.
D has the power to walk away with all of the gold, and A, B, and C dead. He has no incentive to agree to anything less, because if enough votes fail he’ll be in the best possible position. This determines E’s default result, which is what he makes decisions based off of. Building out the game tree helps here.
If B, C, D, and E throw A overboard then C, D, and E are in a position to throw B overboard and any argument B, C, D, and E can come up with for throwing A overboard is just as strong an argument as C, D, and E can come up with for throwing B overboard. In fact, with fewer pirates an even split would be even more advantageous to C, D, and E. So B will always vote for A’s split out of self-preservation. If C throws A overboard he will end up in the same situation as B was originally; needing to support the highest ranking pirate to avoid being the next one up for going overboard. Since the second in command will always vote for the first in command out of self preservation he or she will accept a split with zero coins for themselves. Therefore A only has to offer C 1 coin to get C’s vote. A, B, and C’s majority rules.
In real life I imagine the pirate who is best at up-to-5-way fights is left with 100 coins. If the other pirates were truly rational then they would never have boarded a pirate ship with a pirate who is better at an up-to-5-way fight than them.
When someone asks me how I would get out of a particularly sticky situation, I often fight the urge to glibly respond, by not getting it to said situation.
I digress, if the other pirates were truly rational then they would never let anyone know how good they were at an up-to-X-way fight.
By extension, should truly rational entities never let anyone know how rational they are?
No, they should sometimes not let people know that. Sometimes it is an advantage—either by allowing cooperation that would not otherwise have been possible or demonstrating superior power and so allow options for dominance.
I doubt it. Humans almost never just have an all in winner takes all fight. The most charismatic pirate will end up with the greatest share, while the others end up with lesser shares depending on what it takes for the leader to maintain alliances. (Estimated and observed physical prowess is one component of said charisma in the circumstance).
Well if they chose to decline A’s proposal for whatever reason, that would put C and E in a worse position than if they didn’t.
Outrage over being treated unfairly doesn’t come into one time prisoner’s dilemmata. Each pirate wants to survive with the maximum amount of gold, and C and E would get nothing if they didn’t vote for A’s proposal.
Hence, if C and E were outraged as you suggest, and voted against A’s proposal, they would walk away with even less. One gold coin buys you infinitely more blackjack and hookers than zero gold coins.
If C and E—and I’d say all 4 of them really, at least regarding a 98 0 1 0 1 solution—were inclined to be outraged as I suggest, and A knew this, they would walk away with more money. For me, that trumps any possible math and logic you could put forward.
And just in case A is stupid:
“But look, C and E, this is the optimal solution, if you don’t listen to me you’ll get less gold!”
“Nice try, smartass. Overboard you go.”
B watched on, starting to sweat...
EDIT: Ooops, I notice that I missed the fact that B doesn’t need to sweat since he just needs D. Still, my main point isn’t about B, but A.
Also I wanna make it 100% clear: I don’t claim that the proof is incorrect, given all the assumptions of the problem, including the ones about how the agents work. I’m just not impressed with the agents, with their ability to achieve their goals. Leave A unchanged and toss in 4 reasonably bright real humans as B C D E, at least some of them will leave with more money.
...because it’s very hot in Pirate Island’s shark-infested Pirate Bay, not out of any fear or distress at an outcome that put her in a better position than she had occupied before.
Whereas A had to build an outright majority to get his plan approved, B just had to convince one other pirate. D was the natural choice, both from a strict logico-mathematical view, and because D had just watched C and E team up to throw their former captain overboard. It wasn’t that they were against betraying their superiors for a slice of the treasure, it was that the slice wasn’t big enough! D wasn’t very bright—B knew from sharing a schooner with him these last few months—but team CE had been so obliging as to slice a big branch off D’s decision tree. What was left was a stump. D could take her offer of 1 coin, or be left to the mercy of the outrageously blood-thirsty team CE.
C and E watched on, dreaming of all the wonderful things they could do with their 0 coins.
[I think the “rationality = winning” story holds here (in the case where A’s proposal passes, not in this weird counterfactual cul-de-sac) but in a more subtle way. The 98 0 1 0 1 solution basically gives a value of the ranks, i.e., how much a pirate should be willing to pay to get into that rank at the time treasure will be divided. From this perspective, being A is highly valuable, and A should have been willing to pay, say, 43 coins for his ship, 2 coins for powder, 7 coins for wages to B, C, D, E, etc., to make it into that position. C, on the other hand, might turn down a promotion to second-in-command over B, unless it’s paired with a wage hike of one 1 coin; B would be surprisingly happy to be given such a demotion, if her pay remained unchanged. All the pirates can win even in a 98 0 1 0 1 solution, if they knew such a treasure would be found and planned accordingly.]
It seems to me that the extent to which B C D E will be able to get more money is to some extent dependent on their ability to plausibly precommit to rejecting an “unfair” deal… and possibly their ability to plausibly precommit to accepting a “fair” one.
Emphasis on “plausibly” and “PIRATES.”
At minimum, if they can plausibly precommit to things, I’d expect at the very least CDE to precommit to tossing A B overboard no matter what is offered and splitting the pot three ways. There are quite possibly better commitments to make even than this.
Heh, if I can’t convince you with “any possible math and logic”, let me try with this great video (also that one) that shows the consequences of “reasoning via outrage”.
Watched the first one. It was very different from the scenario we’re discussing. No one’s life was at stake. Also the shares were unequal from the start, so there was no fair scenario being denied, to get outraged about.
I’m not in favor of “reasoning via outrage” in general. I’m simply in favor of possessing a (known) inclination to turn down overly skewed deals (like humans generally have, usefully I might add); if I have it, and your life is at stake, you’d have to be suicidal to propose a 98 0 1 0 1 if I’m one of the people whose vote you need.
What makes it different from the video example is that, in the pirate example, if I turn down the deal the proponent loses far, far more than I do. Not just 98 coins to my 1, but their life, which should be many orders of magnitude more precious. So there’s clearly room for a more fair deal. The woman in that case wasn’t like my proposed E or C, she was like a significantly stupider version of A, wanting an unfairly good deal in a situation when there was no reason for her to believe her commitment could reliably prevail over the other players’ ability to do the same.
A suggestion to randomize was made and denied. They fail at thinking. Especially Jo, who kept trying to convince herself and others that she didn’t care about money. Sour grapes—really pathetic.
Whenever I come across highly counterintuitive claims along these lines, I code them up and see how they perform over many iterations.
This is a lot trickier to do in this case compared to, say, the Monty Hall problem, but if you restricted it just to cases in which Pirate A retained 98 of the coins, you could demonstrate whether the [98, 0, 1, 0, 1] distribution was stable or not.
Also, I’d suggest thinking about this in a slightly different way to the way you’re thinking about it. The only pirate in the scenario who doesn’t have to worry about dying is pirate E, who can make any demands he likes from pirate D. What distribution would he suggest?
Edit: Rereading the wording of the scenario, pirate E can’t make any demands he likes from pirate D, and pirate D himself also doesn’t need to worry about dying.
That shows one aspect of the consequences of reasoning via outrage. It doesn’t indicate that the strategy itself is bad. In a similar way the consequences of randomizing and defending Podunk 1⁄11 times is that 1⁄11 times (against a good player) you will end up on youtube losing Metropolis.
Whoever came up with that game show is a genius.
“I will stand firm on A until A becomes worth less than C is now, then I will accept B or C. You get more by accepting B or C now than you get by trying to get more.”
One rational course of action is to mutually commit to a random split, and follow through. What’s the rational course of action to respond to someone who makes that threat and is believed to follow through on it? If it is known that the other two participants are rational, why isn’t making a threat of that nature rational?