10 ms·

Newcomb's paradox

54 points by monort 12y ago

cwp 12y ago
I always find this kind of philosophical thought experiment unsatisfying. Super-accurate predictions of human behaviour are just not possible. If I could do it, I'd be a gazillionaire philanthropist/playboy dating supermodels and advising heads of state because I can't be bothered to rule the world directly. As it is, I can't do better than a draw against a 5-year-old at rock-paper-scissors. So this paradox tells us more about psychology than philosophy. Folks who think "A and B" is the right answer basically ignore the bit about the predictor never (or almost never) being wrong and go with a strategy that is great for fallible human predictors. And well they should. The only thing more ridiculous than an infallible predictor is one that wastes his time playing shell games where the best he can do is break even.
- davidrusu 12y ago
  I can be more interesting reframed as such: The player is the AI, and the predictor is the AI programmer. The AI programmer can look into the innards of the AI ie. the source code and can thus predict with high accuracy what the AI will do. What is a winning strategy for the AI? Or taken another way, you can have AI's that have access to each other's source code and are competing for some scarce resource, how do you design an AI that 'wins' when it's behaviour is known it's opponent?
  - bluepnume 12y ago
    Sure you can. The AIs behaviour could be as simple as "Always pick box B". The difficult bit would be designing an AI which, given perfect knowledge of its logic, would pick both boxes despite appearing to be more likely to pick only B. In that case, you could simply have an AI with a 0.499999 chance of picking both and a 0.5000001 chance of picking B. The expected winnings would be $1,000,500. But then, once it comes down to probability, the predictor is no longer a 'perfect predictor' any more.
    - atopal 12y ago
      That would probably be counted as a random choice and as the rules state: > if the Predictor predicts that the player will choose randomly, then box B will contain nothing.
- nosmatarmut 12y ago
  I don't think the schism is because of fallible vs infallible so much as people being stuck in naive decision theory (just take both boxes; it's already decided beforehand!) or not (hey, the kinds of decisions I'm willing to make might have changed what Omega decided in the past!). After all, Omega need not be infallible. So long as he predicts your decision with an accuracy of 50.05% (slightly better than a coin toss), you profit: --- Let p be the probability that Omega predicts your decision correctly. E(one-boxing) = p⋅$1mil + (1-p)⋅0 E(two-boxing) = (1-p)⋅$1.01mil + p⋅$1k Solving for E(one-boxing) > E(two-boxing) p⋅$1mil > (1-p)⋅$1.01mil + p⋅$1k p($1mil + $1.01mil - $1k) > $1.01mil p⋅2mil > $1.01mil p > 50.05% --- And if he doesn't predict you slightly better than a coin toss, why is he called the Predictor?
- baddox 12y ago
  It's unsatisfying because it's so poorly defined. As you attempt to define it more precisely, the problem just converges on the problem of whether free will exists.
vilhelm_s 12y ago
Worth mentioning Scott Aaronson's blog post (http://www.scottaaronson.com/blog/?p=30 http://www.scottaaronson.com/blog/?p=30), and a lot of discussion on Less Wrong over the years (http://wiki.lesswrong.com/wiki/Newcomb%27s_problem http://wiki.lesswrong.com/wiki/Newcomb%27s_problem).
fitter 12y ago
I guess this boils down to whether you believe in determinism. If you do, then the predictor will always be right, and you have essentially zero chance of fooling it by "changing your mind" later for the extra money. If you don't believe in such a thing, then theoretically some nondeterministic volition of yours could allow you to change your mind in a way that the predictor could not have deterministically forseen.
- justzisguyuknow 12y ago
  It reminds me of the 'Battle of Wits' scene in The Princess Bride: http://c2.com/cgi/wiki?BattleOfWits http://c2.com/cgi/wiki?BattleOfWits
- Houshalter 12y ago
  That's not really the point of the thought experiment at all. And invoking randomness doesn't make the thought experiment easier, just more complicated. From the link someone posted above: >(Incidentally, don’t imagine you can wiggle out of this by basing your decision on a coin flip! For suppose the Predictor predicts you’ll open only the first box with probability p. Then he’ll put the $1,000,000 in that box with the same probability p. So your expected payoff is 1,000,000p2 + 1,001,000p(1-p) + 1,000(1-p)2 = 1,000,000p + 1,000(1-p), and you’re stuck with the same paradox as before.)
- empthought 12y ago
  It's not about changing your mind for the money, it's about the fact that causality doesn't (shouldn't) run backwards in time. Consider this: when you are faced with the choice, the allotted money is already under the boxes. How could what you choose now affect this outcome? It can't. You must always take both boxes to get the maximum amount of money possible. Either the $1,000,000 is under the single box, or it is not. If you take both boxes, you will get $1000 regardless of anything else, and possibly $1,001,000. If you take the single box, you will either get $0 or $1,000,000, but your action can't possibly change that, unless you believe somehow that causality runs backwards in time.
  - Retric 12y ago
_greim_ 12y ago
I think there's a weak echo of this concept that plays out in an election. Except swap in the inconvenience of voting for giving up the $1,000 box. On the one hand, why bother voting? It's a pain in the ass and my single vote has such a negligible effect. On the other hand, if everyone like me has that same attitude, then I and others like me lose our voice in the election. So should I vote, or not?
- baddox 12y ago
  That's a fairly simple one. If all you value is the benefits to you of your influence on the election, do not bother to vote (and especially don't bother spending the resources required to educate yourselves so as to vote responsibly). It's very clearly not worth it except perhaps for the smallest local elections or closest large elections. If you value other things related to voting, like feeling as if you've done your civic duty, or feeling like a member of a group (like a political party), then by all means vote if the hassle of physically voting is less than that benefit. This seems like a pretty clear description of rational behavior, and if you expect people to behave largely rationally, this description seems to explain some of the problems often attributed to elections, like low voter participation and low voter knowledge of the candidates and issues.
  - SilasX 12y ago
    But then if people only care about the benefits to them, then they'll be overtaken by "lizards" who exploit them but never get voted out because no one thinks voting passes a CBA. Populations who vote "despite" its wastefulness systematically win against those who don't. Arguably, the only reason any population isn't overrun by lizards is because it's people are mostly "wasteful" in this sense. One intermediate solution is to force everyone to vote so that it's no longer costly. This is arguably what is accomplished when people promote voting out of civic duty, etc.
    - baddox 12y ago
      But I don't think people are wasteful in that sense. Voter participation and voter awareness tends to be low, at least in the USA. Besides, if your government only works if people act in a specific irrational manner, I don't have high hopes for it, especially considering that one usually cited fundamental role of government is to fix problems where individual rationality does not lead to group rationality. Forcing people to vote doesn't incentivize people to educate themselves on the issues, which is required to "vote responsibly" according to the usual Western civics class description of how democracy is supposed to work.
greggyb 12y ago
For the risk-averse: Make a bet with someone for $500,000.00 that you can prove The Predictor is fallible. Take only box B. If box B contains $1,000,000.00, then you have lost the bet and you are left with only $500,000.00. If box B contains no money, you have wone the bet and are left with $500,000.00.
- empthought 12y ago
  Mmm credit default swap.
- baddox 12y ago
  Who would take the other side of that bet?
  - lobe 12y ago
    Since it is a rule of the game that the predictor is infallible, anyone with $500,000 would take that
    - empthought 12y ago
      It's not a rule of the game that the predictor is infallible, only that it's very likely to be correct.
      - greggyb 12y ago
        It seems there are multiple versions of the paradox. It does seem reasonable that you can find someone to take the bet for <$999K if it is known that The Predictor is "very likely to be correct". Any bet amount <$999K is qualitatively the same as my original $500K suggestion, you increase your guaranteed minimum by decreasing your potential maximum without having to resolve the paradox.
        empthought 12y ago
        I think any version of the paradox that defines the predictor as infallible misses the whole point of the paradox. That's just defining the outcome of the game as the will of God. "Has always been observed to be correct" is the appropriate construction. However, I think someone could resuscitate the original intent of the paradox by having the Predictor's actions also hinge on whether or not it predicts that you would make such a bet, and leave box B empty if it does predict that. Essentially defining itself to be correct in the situation where, without this addendum, it would have been incorrect and you would have won the bet.
altrego99 12y ago
Not sure why it is a paradox - assuming the predictor is superintelligent, you don't try to fool it. By definition its intelligence can predict what you will do in the very last moment, so the fact that it doesn't get to change anything once prediction is made, is immaterial.
- davidrusu 12y ago
  Let's reverse the numbers and make both boxes transparent. If The Predictor suspects you will choose just box A, it'll put 1 million in box B and 1 thousand in box A, if it suspects you will take both A and B, it will put nothing anything in box B and 1 thousand in box A. So now you standing in front of the two transparent boxes. You see that there is $1 million in box B, yet you still take just box A?
  - nosmatarmut 12y ago
    In that scenario, it wouldn't make a difference what you choose. If you were so inclined to take Box B's million, Omega would never have put that million in the first place. The only way for Omega to put that million there is if you weren't inclined to take Box B - despite the million being completely visible to you - in which case you lose anyway. The situation where Omega gives you the million, and you take it, just never comes up. Can't fool it.
  - anon4 12y ago
    In that case, Box B would only be full if you're a very honest person, who'll take only Box B.
  - altrego99 12y ago
    In that scenario, the predictor will always "predict" that you will take both boxes. The lack of information of box B, is exactly what makes the other case different. Then you need to only rely on thinking and you do not know if box B has a million dollars till you open it. If you risk taking two boxes, you will lose it. --- Let me give another example to make the original scenario transparent. Imagine I will write a function "decide(double content_of_A)" to decide whether B or both will be opened, given content of A. Imagine you can examine the function beforehand, and you are super-intelligent compared to me, so any attempt to obfuscate the code in my part will be utterly useless and easily seen through. And you are honest - in putting the $1M in box B if your analysis suggests that the decision function will only take B. Note that my function gets called after you have placed the money, just as in the original scenario. Would I not write the function to choose B? I would.
mietek 12y ago
> When formulated using Bayesian networks, two standard decision algorithms (Evidential Decision Theory and Causal Decision Theory) can be shown to fail systematically when faced with aspects of the prisoner’s dilemma and so-called “Newcomblike” problems. We describe a new form of decision algorithm, called Timeless Decision Theory, which consistently wins on these problems. — Alex Altair, MIRI, “A Comparison of Decision Algorithms on Newcomblike Problems” https://intelligence.org/files/Comparison.pdf https://intelligence.org/files/Comparison.pdf
fiatmoney 12y ago
The standard "solution" (that isn't really a solution, but an explanation) is that the predictor has decided to reward the kind of person who one-boxes, and is extremely good at predicting whether you are that kind of person (perhaps even better than you yourself are). So, if you can "decide to be the kind of person" who one-boxes (and perhaps by induction "decide to be the kind of person who decides to be a certain kind of person"), you can make out pretty well.
samatman 12y ago
Via Turing, we know that the Predictor would be able to decide programs, and since it can't, it can't be a Predictor. The isomorphism between the program which defeats decidability and the two-box Newcomb problem is left as an exercise.
- connerbrooks 12y ago
  I think this may be the proof. Start by assuming that the predictor is a decider P for a computational model of a human M in a situation encoded by w. We can then construct a Turing Machine S that decides A_TM. S <M, w> { 1. Run P on w. 2. If P halts, run M on w; if M accepts, accept, if it rejects reject. } Since S decides A_TM we must have made a mistake somewhere in our proof, our only mistake could be that the predictor P is a decider. Therefore the Predictor is not a decider.
  - samatman 12y ago
    Full marks!
- jcoffland 12y ago
  You assume that a human cannot be described with something less powerful than a Turing machine. There is no reason to believe that knowing what a human will do in this instance is equal to decidability of computer programs.
  - Dylan16807 12y ago
    I almost objected, but you're right. The human has finite time with which to calculate. The predictor can easily be assumed to have more time. There's no problem calculating if a program will halt in finite time.
  - samatman 12y ago
    I assume nothing of the sort. I merely assume that humans, like computers, are capable of evaluating the truth of something and then deliberately reporting the opposite. That is all that is required.
olalonde 12y ago
I like Scott Aaronson's solution (http://www.scottaaronson.com/blog/?p=30 http://www.scottaaronson.com/blog/?p=30). Basically, assuming: 1) completely infallible and incapable of error 2) to get a perfect prediction, the predictor must simulate you perfectly to the extent that the simulated you won't have any way to know it is the simulation Therefore, at the time of the decision, "you" might actually be the "simulated you" and any decision you make will indeed affect the content of the boxes for the "real you". Which makes single boxing the rational decision.
hbinvygx 12y ago
Maps
deleted 12y ago
[deleted]
eli_gottlieb 12y ago
It's not a paradox to those who understand compatibilist free will, and how basic information-sharing means that events at two different points in time and space can be isomorphic. There's no impossibility being committed, and no retrocausality either.
sixQuarks 12y ago
What I don't understand is why would anyone risk taking both A & B just to gain a measly $1,000? Just take the million and be happy with it.

54 points by monort 12y ago

cwp 12y ago

I always find this kind of philosophical thought experiment unsatisfying. Super-accurate predictions of human behaviour are just not possible. If I could do it, I'd be a gazillionaire philanthropist/playboy dating supermodels and advising heads of state because I can't be bothered to rule the world directly. As it is, I can't do better than a draw against a 5-year-old at rock-paper-scissors. So this paradox tells us more about psychology than philosophy. Folks who think "A and B" is the right answer basically ignore the bit about the predictor never (or almost never) being wrong and go with a strategy that is great for fallible human predictors. And well they should. The only thing more ridiculous than an infallible predictor is one that wastes his time playing shell games where the best he can do is break even.

davidrusu 12y ago
I can be more interesting reframed as such: The player is the AI, and the predictor is the AI programmer. The AI programmer can look into the innards of the AI ie. the source code and can thus predict with high accuracy what the AI will do. What is a winning strategy for the AI? Or taken another way, you can have AI's that have access to each other's source code and are competing for some scarce resource, how do you design an AI that 'wins' when it's behaviour is known it's opponent?
- bluepnume 12y ago
  Sure you can. The AIs behaviour could be as simple as "Always pick box B". The difficult bit would be designing an AI which, given perfect knowledge of its logic, would pick both boxes despite appearing to be more likely to pick only B. In that case, you could simply have an AI with a 0.499999 chance of picking both and a 0.5000001 chance of picking B. The expected winnings would be $1,000,500. But then, once it comes down to probability, the predictor is no longer a 'perfect predictor' any more.
  - atopal 12y ago
    That would probably be counted as a random choice and as the rules state: > if the Predictor predicts that the player will choose randomly, then box B will contain nothing.
nosmatarmut 12y ago
I don't think the schism is because of fallible vs infallible so much as people being stuck in naive decision theory (just take both boxes; it's already decided beforehand!) or not (hey, the kinds of decisions I'm willing to make might have changed what Omega decided in the past!). After all, Omega need not be infallible. So long as he predicts your decision with an accuracy of 50.05% (slightly better than a coin toss), you profit: --- Let p be the probability that Omega predicts your decision correctly. E(one-boxing) = p⋅$1mil + (1-p)⋅0 E(two-boxing) = (1-p)⋅$1.01mil + p⋅$1k Solving for E(one-boxing) > E(two-boxing) p⋅$1mil > (1-p)⋅$1.01mil + p⋅$1k p($1mil + $1.01mil - $1k) > $1.01mil p⋅2mil > $1.01mil p > 50.05% --- And if he doesn't predict you slightly better than a coin toss, why is he called the Predictor?
baddox 12y ago
It's unsatisfying because it's so poorly defined. As you attempt to define it more precisely, the problem just converges on the problem of whether free will exists.

vilhelm_s 12y ago

Worth mentioning Scott Aaronson's blog post (http://www.scottaaronson.com/blog/?p=30 http://www.scottaaronson.com/blog/?p=30), and a lot of discussion on Less Wrong over the years (http://wiki.lesswrong.com/wiki/Newcomb%27s_problem http://wiki.lesswrong.com/wiki/Newcomb%27s_problem).

fitter 12y ago

I guess this boils down to whether you believe in determinism. If you do, then the predictor will always be right, and you have essentially zero chance of fooling it by "changing your mind" later for the extra money. If you don't believe in such a thing, then theoretically some nondeterministic volition of yours could allow you to change your mind in a way that the predictor could not have deterministically forseen.

justzisguyuknow 12y ago
It reminds me of the 'Battle of Wits' scene in The Princess Bride: http://c2.com/cgi/wiki?BattleOfWits http://c2.com/cgi/wiki?BattleOfWits
Houshalter 12y ago
That's not really the point of the thought experiment at all. And invoking randomness doesn't make the thought experiment easier, just more complicated. From the link someone posted above: >(Incidentally, don’t imagine you can wiggle out of this by basing your decision on a coin flip! For suppose the Predictor predicts you’ll open only the first box with probability p. Then he’ll put the $1,000,000 in that box with the same probability p. So your expected payoff is 1,000,000p2 + 1,001,000p(1-p) + 1,000(1-p)2 = 1,000,000p + 1,000(1-p), and you’re stuck with the same paradox as before.)
empthought 12y ago
It's not about changing your mind for the money, it's about the fact that causality doesn't (shouldn't) run backwards in time. Consider this: when you are faced with the choice, the allotted money is already under the boxes. How could what you choose now affect this outcome? It can't. You must always take both boxes to get the maximum amount of money possible. Either the $1,000,000 is under the single box, or it is not. If you take both boxes, you will get $1000 regardless of anything else, and possibly $1,001,000. If you take the single box, you will either get $0 or $1,000,000, but your action can't possibly change that, unless you believe somehow that causality runs backwards in time.
- Retric 12y ago

_greim_ 12y ago

I think there's a weak echo of this concept that plays out in an election. Except swap in the inconvenience of voting for giving up the $1,000 box. On the one hand, why bother voting? It's a pain in the ass and my single vote has such a negligible effect. On the other hand, if everyone like me has that same attitude, then I and others like me lose our voice in the election. So should I vote, or not?

baddox 12y ago
That's a fairly simple one. If all you value is the benefits to you of your influence on the election, do not bother to vote (and especially don't bother spending the resources required to educate yourselves so as to vote responsibly). It's very clearly not worth it except perhaps for the smallest local elections or closest large elections. If you value other things related to voting, like feeling as if you've done your civic duty, or feeling like a member of a group (like a political party), then by all means vote if the hassle of physically voting is less than that benefit. This seems like a pretty clear description of rational behavior, and if you expect people to behave largely rationally, this description seems to explain some of the problems often attributed to elections, like low voter participation and low voter knowledge of the candidates and issues.
- SilasX 12y ago
  But then if people only care about the benefits to them, then they'll be overtaken by "lizards" who exploit them but never get voted out because no one thinks voting passes a CBA. Populations who vote "despite" its wastefulness systematically win against those who don't. Arguably, the only reason any population isn't overrun by lizards is because it's people are mostly "wasteful" in this sense. One intermediate solution is to force everyone to vote so that it's no longer costly. This is arguably what is accomplished when people promote voting out of civic duty, etc.
  - baddox 12y ago
    But I don't think people are wasteful in that sense. Voter participation and voter awareness tends to be low, at least in the USA. Besides, if your government only works if people act in a specific irrational manner, I don't have high hopes for it, especially considering that one usually cited fundamental role of government is to fix problems where individual rationality does not lead to group rationality. Forcing people to vote doesn't incentivize people to educate themselves on the issues, which is required to "vote responsibly" according to the usual Western civics class description of how democracy is supposed to work.

greggyb 12y ago

For the risk-averse: Make a bet with someone for $500,000.00 that you can prove The Predictor is fallible. Take only box B. If box B contains $1,000,000.00, then you have lost the bet and you are left with only $500,000.00. If box B contains no money, you have wone the bet and are left with $500,000.00.

empthought 12y ago
Mmm credit default swap.
baddox 12y ago
Who would take the other side of that bet?
- lobe 12y ago
  Since it is a rule of the game that the predictor is infallible, anyone with $500,000 would take that
  - empthought 12y ago
    It's not a rule of the game that the predictor is infallible, only that it's very likely to be correct.
    - greggyb 12y ago
      It seems there are multiple versions of the paradox. It does seem reasonable that you can find someone to take the bet for <$999K if it is known that The Predictor is "very likely to be correct". Any bet amount <$999K is qualitatively the same as my original $500K suggestion, you increase your guaranteed minimum by decreasing your potential maximum without having to resolve the paradox.
      - empthought 12y ago
        I think any version of the paradox that defines the predictor as infallible misses the whole point of the paradox. That's just defining the outcome of the game as the will of God. "Has always been observed to be correct" is the appropriate construction. However, I think someone could resuscitate the original intent of the paradox by having the Predictor's actions also hinge on whether or not it predicts that you would make such a bet, and leave box B empty if it does predict that. Essentially defining itself to be correct in the situation where, without this addendum, it would have been incorrect and you would have won the bet.

altrego99 12y ago

Not sure why it is a paradox - assuming the predictor is superintelligent, you don't try to fool it. By definition its intelligence can predict what you will do in the very last moment, so the fact that it doesn't get to change anything once prediction is made, is immaterial.

davidrusu 12y ago
Let's reverse the numbers and make both boxes transparent. If The Predictor suspects you will choose just box A, it'll put 1 million in box B and 1 thousand in box A, if it suspects you will take both A and B, it will put nothing anything in box B and 1 thousand in box A. So now you standing in front of the two transparent boxes. You see that there is $1 million in box B, yet you still take just box A?
- nosmatarmut 12y ago
  In that scenario, it wouldn't make a difference what you choose. If you were so inclined to take Box B's million, Omega would never have put that million in the first place. The only way for Omega to put that million there is if you weren't inclined to take Box B - despite the million being completely visible to you - in which case you lose anyway. The situation where Omega gives you the million, and you take it, just never comes up. Can't fool it.
- anon4 12y ago
  In that case, Box B would only be full if you're a very honest person, who'll take only Box B.
- altrego99 12y ago
  In that scenario, the predictor will always "predict" that you will take both boxes. The lack of information of box B, is exactly what makes the other case different. Then you need to only rely on thinking and you do not know if box B has a million dollars till you open it. If you risk taking two boxes, you will lose it. --- Let me give another example to make the original scenario transparent. Imagine I will write a function "decide(double content_of_A)" to decide whether B or both will be opened, given content of A. Imagine you can examine the function beforehand, and you are super-intelligent compared to me, so any attempt to obfuscate the code in my part will be utterly useless and easily seen through. And you are honest - in putting the $1M in box B if your analysis suggests that the decision function will only take B. Note that my function gets called after you have placed the money, just as in the original scenario. Would I not write the function to choose B? I would.

mietek 12y ago

> When formulated using Bayesian networks, two standard decision algorithms (Evidential Decision Theory and Causal Decision Theory) can be shown to fail systematically when faced with aspects of the prisoner’s dilemma and so-called “Newcomblike” problems. We describe a new form of decision algorithm, called Timeless Decision Theory, which consistently wins on these problems. — Alex Altair, MIRI, “A Comparison of Decision Algorithms on Newcomblike Problems” https://intelligence.org/files/Comparison.pdf https://intelligence.org/files/Comparison.pdf

fiatmoney 12y ago

The standard "solution" (that isn't really a solution, but an explanation) is that the predictor has decided to reward the kind of person who one-boxes, and is extremely good at predicting whether you are that kind of person (perhaps even better than you yourself are). So, if you can "decide to be the kind of person" who one-boxes (and perhaps by induction "decide to be the kind of person who decides to be a certain kind of person"), you can make out pretty well.

samatman 12y ago

Via Turing, we know that the Predictor would be able to decide programs, and since it can't, it can't be a Predictor. The isomorphism between the program which defeats decidability and the two-box Newcomb problem is left as an exercise.

connerbrooks 12y ago
I think this may be the proof. Start by assuming that the predictor is a decider P for a computational model of a human M in a situation encoded by w. We can then construct a Turing Machine S that decides A_TM. S <M, w> { 1. Run P on w. 2. If P halts, run M on w; if M accepts, accept, if it rejects reject. } Since S decides A_TM we must have made a mistake somewhere in our proof, our only mistake could be that the predictor P is a decider. Therefore the Predictor is not a decider.
- samatman 12y ago
  Full marks!
jcoffland 12y ago
You assume that a human cannot be described with something less powerful than a Turing machine. There is no reason to believe that knowing what a human will do in this instance is equal to decidability of computer programs.
- Dylan16807 12y ago
  I almost objected, but you're right. The human has finite time with which to calculate. The predictor can easily be assumed to have more time. There's no problem calculating if a program will halt in finite time.
- samatman 12y ago
  I assume nothing of the sort. I merely assume that humans, like computers, are capable of evaluating the truth of something and then deliberately reporting the opposite. That is all that is required.

olalonde 12y ago

I like Scott Aaronson's solution (http://www.scottaaronson.com/blog/?p=30 http://www.scottaaronson.com/blog/?p=30). Basically, assuming: 1) completely infallible and incapable of error 2) to get a perfect prediction, the predictor must simulate you perfectly to the extent that the simulated you won't have any way to know it is the simulation Therefore, at the time of the decision, "you" might actually be the "simulated you" and any decision you make will indeed affect the content of the boxes for the "real you". Which makes single boxing the rational decision.

hbinvygx 12y ago

Maps

deleted 12y ago

[deleted]

eli_gottlieb 12y ago

It's not a paradox to those who understand compatibilist free will, and how basic information-sharing means that events at two different points in time and space can be isomorphic. There's no impossibility being committed, and no retrocausality either.

sixQuarks 12y ago

What I don't understand is why would anyone risk taking both A & B just to gain a measly $1,000? Just take the million and be happy with it.