Darth_Pugwash
wobble wobble
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This was a fun thread... I'd still one box it. It's not the intuitive choice, but statistically at least it's the way to go.
Newcomb's Problem
- Thread starter Erik Mesoy
- Start date
Perfection
The Great Head.
So I've thought about this a little bit more and I've come to a couple conclusions:
1. One boxing must be the correct answer. It is an undeniable fact that those with the one box strategy makes more money. I cannot see how those who do not have the best outcome have the best strategy It seems to me that by definition the best strategy is the one that gives the best outcome. The challenge then becomes to square this with other truths.
2. The key to coming up with a good account lies in personal identity. And the rejection of the notion that "you" are only a being here in the present about to make a box opening decision. That represents a naive illusion.
I'm curious about how Two Boxers would take to the following related conundrum:
In the future, people can be duplicated to a practically exact level of detail. Because you have very special skills your employer says that you are to be duplicated (and you agree with this) and you and your duplicate will be assigned (randomly) to two different positions (let's say one on Mars, and one on Venus).
Immediately after duplication (it's performed while you are unconscious), you and your duplicate awake to see your mischievous friend (who is the machine operator) on a video screen saying, "you and your double are in rooms that are practically exactly the same, listening to this message, both rooms have two buttons, if you push the red button I will give your double $2,000,000, if you push the blue button I will give you $1,000,000".
He adds, "if your double pushes the red button I will give you $2,000,000, if your double pushes the blue button I will give him $1,000,000"
"I will give you both 15 minutes to make your decision, after which I will let you guys out and give you each the money from you and your double's button pushing"
What button would you push?
1. One boxing must be the correct answer. It is an undeniable fact that those with the one box strategy makes more money. I cannot see how those who do not have the best outcome have the best strategy It seems to me that by definition the best strategy is the one that gives the best outcome. The challenge then becomes to square this with other truths.
2. The key to coming up with a good account lies in personal identity. And the rejection of the notion that "you" are only a being here in the present about to make a box opening decision. That represents a naive illusion.
I'm curious about how Two Boxers would take to the following related conundrum:
In the future, people can be duplicated to a practically exact level of detail. Because you have very special skills your employer says that you are to be duplicated (and you agree with this) and you and your duplicate will be assigned (randomly) to two different positions (let's say one on Mars, and one on Venus).
Immediately after duplication (it's performed while you are unconscious), you and your duplicate awake to see your mischievous friend (who is the machine operator) on a video screen saying, "you and your double are in rooms that are practically exactly the same, listening to this message, both rooms have two buttons, if you push the red button I will give your double $2,000,000, if you push the blue button I will give you $1,000,000".
He adds, "if your double pushes the red button I will give you $2,000,000, if your double pushes the blue button I will give him $1,000,000"
"I will give you both 15 minutes to make your decision, after which I will let you guys out and give you each the money from you and your double's button pushing"
What button would you push?
No, Perfection, you're not understanding the two boxer position. Two boxers would not be different in their choices than one boxers here. Externalizing the self is not the issue.
The two boxer argument comes from the fact that choosing both boxes does not cause the oracle to do anything. No action taken when picking the boxes can effect the outcome. So whatever the chance that there is money in box B, that is fixed. The utility of choosing both boxes is based only the things that are caused by the choice itself. So the benefit of choosing one box is $0 + whatever is in box A. The benefit of choosing both boxes is $1000 + whatever is in box A. The second choice is always better by this logic.
On a different note, I wonder if there is a correlation between the results of this poll and voter turn out in politics. It seems to me that one boxers should believe their vote counts more than two boxers. Both categories would have people who agree that our individual vote doesn't mean anything when you vote, since the difference between the candidates is always much larger than any single vote. But I think a one boxer would be more willing to say that an despite this lack of causality between a single vote and the election result, voting is still prudent if you want your candidate elected.
The two boxer argument comes from the fact that choosing both boxes does not cause the oracle to do anything. No action taken when picking the boxes can effect the outcome. So whatever the chance that there is money in box B, that is fixed. The utility of choosing both boxes is based only the things that are caused by the choice itself. So the benefit of choosing one box is $0 + whatever is in box A. The benefit of choosing both boxes is $1000 + whatever is in box A. The second choice is always better by this logic.
On a different note, I wonder if there is a correlation between the results of this poll and voter turn out in politics. It seems to me that one boxers should believe their vote counts more than two boxers. Both categories would have people who agree that our individual vote doesn't mean anything when you vote, since the difference between the candidates is always much larger than any single vote. But I think a one boxer would be more willing to say that an despite this lack of causality between a single vote and the election result, voting is still prudent if you want your candidate elected.
Perfection
The Great Head.
Well, let's let some two boxers answer!
I disagree!
Just like choosing the blue button does not (at least with the naive view of self) cause your double to do anything.
You (naively) cannot effect what your double will do, either. Either he pushes the blue or red button, you have no control.
The same argument can be made for the double case, if you pick blue you will get $1,000,000 plus whatever your double picks if you pick red you'll get 0 plus whatever your double picks.
Yes, but in your scenario there is no sizable disadvantage to choosing the blue button. So at worst, choosing red is not worse then blue, and at best altruism and kinship with your double results in a net gain for choosing red.
EDIT:
But that did clarify your point. That's what got me thinking about voting, since I was thinking along similar lines, if not realizing that that was the point you were trying to make.
EDIT:
But that did clarify your point. That's what got me thinking about voting, since I was thinking along similar lines, if not realizing that that was the point you were trying to make.
Perfection
The Great Head.
You can agree with all that but disagree with the conclusion? The parallels are perfect!
You don't get a million bucks. That's sizeable. Anyways, you don't think the answer depends on simple scaling of how much more red is worth than blue do you?
(especially because in this case the two box analogue actually gets relatively more money to the one box analogue)As I look at this this has nothing to do with kinship and altruism. I choose red because I know that my double will pick the same as I do, and therefore I will get more money. It has nothing to do with altruism (that's why I think my SimPerfs idea earlier, while interesting really didn't get at the heart of the issue), it has to do with my double and I sharing an aspect of "me-ness".
But from the two box mindset, you don't cause yourself to get the additional million dollars. You only cause your double to get the money. With that outlook there is no direct monetary benefit for choosing the red button. Altruism plays a role. The shared "me-ness" is only a kinship that is of the same sort as you would provide to family, much like if the money were going to your favorite uncle instead of your double. But double or favorite uncle the result would be the same: choose the red button.
Catharsis
catch u on the flip scythe
Both options give the same payoff of zero boxes so it doesn't really matter what you do.
Kennigit
proud 2 boxer
Wait perfy, I don't see a loss of money with that scenario.
I press red, my awesome more-than-a-broski presses red, we get 4 million?
Or if I press red he press blue, I get 0 mil and he gets 3 mil? Both mes presumably pick red and will contact the other to split the money. Or even if he doesn't, we split the 3 mil into 1.5 apiece.
Simple math solves that--according to the rules of the game you are GUARENTEED a payout. I.e. if someone picks red, someone gets paid. Might not be me, but money is determined based on the players choice
The difference is that those boxes has no guarentee what are in them--Omega put whatever he wanted in them. He could have put in bandaids in the "1 million" dollar box for all I know. So, I take both and get both contents. The money was determined by Omega, and the player's choice has 0 relevance.
I press red, my awesome more-than-a-broski presses red, we get 4 million?
Or if I press red he press blue, I get 0 mil and he gets 3 mil? Both mes presumably pick red and will contact the other to split the money. Or even if he doesn't, we split the 3 mil into 1.5 apiece.
Simple math solves that--according to the rules of the game you are GUARENTEED a payout. I.e. if someone picks red, someone gets paid. Might not be me, but money is determined based on the players choice
The difference is that those boxes has no guarentee what are in them--Omega put whatever he wanted in them. He could have put in bandaids in the "1 million" dollar box for all I know. So, I take both and get both contents. The money was determined by Omega, and the player's choice has 0 relevance.
JerichoHill
Bedrock of Knowledge
First Perfection your example is a bad one, in that there is a dominant strategy in blue and red button pressing. It is a boring game. Both players have a dominant strategy to pick blue. Game Theory 101.
Now, onto the original box example. What's the utility to me of an extra 1000 or a n probablity chance of 1000000? Given expectations and what I know about the utility functions, its probably the latter.
Now, onto the original box example. What's the utility to me of an extra 1000 or a n probablity chance of 1000000? Given expectations and what I know about the utility functions, its probably the latter.
Darth_Pugwash
wobble wobble
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One boxer fo' life, yo. I guess I have to echo Perf in saying that I can't grasp why one would two-box when it's one-boxing that consistently pays out the big money.
It's the end results that define the sucess of a strategy. In this case it's a pretty simple test - the object is to get as much money as possible. If two-boxing gives less money than one-boxing, then it's not at all clear how one can defend two-boxing as the superior strategy.
The intuitive response is to think that going for both boxes is always the best idea, because you will always get the contents of both boxes and hence get the maximum possible return. However the scenario more-or-less explicitly rules this out as an effective strategy; in fact, one-boxing gives the better return. What one expects to be the case intuitively is - in the magical world of the hypothetical - nonsense. So if you want win the silly game you have to play by it's own rules and not by the ones you have in your head; that is, observation has to trump intuition or else you're going home with the B-prize.
It's the end results that define the sucess of a strategy. In this case it's a pretty simple test - the object is to get as much money as possible. If two-boxing gives less money than one-boxing, then it's not at all clear how one can defend two-boxing as the superior strategy.
The intuitive response is to think that going for both boxes is always the best idea, because you will always get the contents of both boxes and hence get the maximum possible return. However the scenario more-or-less explicitly rules this out as an effective strategy; in fact, one-boxing gives the better return. What one expects to be the case intuitively is - in the magical world of the hypothetical - nonsense. So if you want win the silly game you have to play by it's own rules and not by the ones you have in your head; that is, observation has to trump intuition or else you're going home with the B-prize.
Onionsoilder
Reaver
- Joined
- Mar 19, 2007
- Messages
- 3,173
Game Theory is not accurate though. It relies exclusively on both players being selfish and uncaring (or untrusting) with the other parties involved. While logically it is the best choice(Gaining 3 or 1 over 2 or 0) in practice it does not always adhere to that standard. In the following situation for example, if both players were somewhat altruistic, they may both pick red on the virtue of providing for their double, who is in essence themselves.
There is a reason that people care for the elderly, sick and disabled even though it grants them nothing, and that reason is not Game Theory.
Mise
isle of lucy
In perfy's scenario I'd pick red, obviously, because I know that the other guy (i.e. me) is also gonna pick red, for the same reason.
The assumption I'm making here is that my decision making process is deterministic and doesn't contain any random component -- that, given identical inputs, my brain will produce identical outputs. I can't rule out human brains are wired with a random number generator, though.
The assumption I'm making here is that my decision making process is deterministic and doesn't contain any random component -- that, given identical inputs, my brain will produce identical outputs. I can't rule out human brains are wired with a random number generator, though.
Kennigit
proud 2 boxer
Dere ain't nuthin magic 'bout Omega boi.
He may be all edumicated but he ain't gonna change the laws of physics. Nor is he gonna be changing my stuff: "Box B is already empty or already full".
Observation 1: box B is currently full or not
Observation 2: box B will still be full or not after my choice
Fact1: taking both boxes gets money in both boxes.
QED'd son.
Mathilda
Queen
Did I observe the 100 instances of Omega getting it right or was I just told about it?
If I observed, I'll take B, if I was told I take both.
And press the red button, same reason as Mise, I know me.
If I observed, I'll take B, if I was told I take both.
And press the red button, same reason as Mise, I know me.
Ayatollah So
the spoof'll set you free
'zactly. Game Theory's premises are unreliable (technically, untrue, but in practice, true enough in many but not all cases) whether interpreted descriptively or normatively. We should consider both de jure premises (those explicitly incorporated into game theory) and de facto premises (those that go into game theory as applied by the vast majority of its users). The selfishness assumption is one of those de facto premises: assuming that utility functions* can be stated without essential reference to each other. The assumption of distrust is another - ignoring the ways in which the utility functions* of each player actually depends on the previous moves of the other.
*Let's pretend that there are such things
Oh, and dominant strategy: for the non-Omega player in the original problem, the "dominant strategy" is to two-box. But it's still the wrong move.
warpus
In pork I trust
That's actually a very good point. I concur, and agree.
Not true. It's actually more of a psychological test to see if you are a trustworthy person. I know I could trust my double to follow the smart strategy and hand over half the money afterwards, so I would press red.
As for the box, it is simply a predetermined intelligence test. The alien just figures out if you are intelligent enough to choose one box. If you are, he puts the one million in there.
Perfection
The Great Head.
I will be replying to others soon.
2008 Perf:
This is similar to my one-box argument of SimPerfs where desire to be Good to RealPerfs provides the motivation to one box it. So, if you believe in Red-buttoning, why not one-boxing?
2010 Perf:
Altruism has nothing to do with it! It all has to do with coordinated action. Let's contrast it with the scenario where only you have the blue and red buttons and your double has none (either you get 1M$ or your double gets 2M$). Suddenly this game becomes quite different! Would you still give your double $2M, if he could not return the favor?
So there's two responses here, one from 2008 Perf, and one from 2010 Perf.
2008 Perf:
This is similar to my one-box argument of SimPerfs where desire to be Good to RealPerfs provides the motivation to one box it. So, if you believe in Red-buttoning, why not one-boxing?
2010 Perf:
Altruism has nothing to do with it! It all has to do with coordinated action. Let's contrast it with the scenario where only you have the blue and red buttons and your double has none (either you get 1M$ or your double gets 2M$). Suddenly this game becomes quite different! Would you still give your double $2M, if he could not return the favor?
