Newcomb's paradox

Discussion in 'General Philosophy' started by James R, Jan 25, 2017.

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Would you choose to take Box B only, or to take both boxes A and B?

This poll will close on Jan 25, 2018 at 7:08 AM.
  1. Take Box B only.

  2. Take both boxes (A and B).

  3. I would try to randomise the decision process and let someone/something else decide for me.

  4. I can't decide how to choose, so I would refuse to play and go home with no money at all.

  5. I refuse on principle to play silly philsophical games, so I would go home with no money at all.

Results are only viewable after voting.
  1. James R Just this guy, you know? Staff Member

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    This came up in another thread. We might as well run a sciforums poll on it to see what people here would do.

    Here's the scenario:

    You are invited to play Pick-a-Box on an unusual TV game show. As a contestant, you are presented with two boxes, A and B. You are told that box A contains $1,000. Box B, on the other hand, contains either $1 million, or nothing. Box A is actually transparent, so you can see the thousand dollars sitting inside. Box B is opaque; you can't look inside it until after you've made a choice.

    Your task is to choose whether you will take either Box B only, or take both boxes (A and B).

    Here's the catch: Pick-a-Box employs a Superintelligent Predictor (the 'SIP'). You are told that prior to your appearance on the show, the SIP conducted an expert, detailed analysis of your personality and of the all possible methods you, personally, might use to make your choice. The SIP then loaded the boxes according to its prediction of your choice, as follows:

    If the SIP predicted you would choose Box B only, it put $1 million in box B.
    If, on the other hand, the SIP predicted you would choose both boxes, then it left box B empty.​

    The prediction by the SIP was made before the taping of the show, and the loading of the two boxes (in particular, box B, containing either $1 million or nothing) was also done before you arrived at the studio (and the boxes have at no time been tampered with after they were loaded in accordance with the SIP's prediction).

    This Pick-a-Box show has been running daily for years, and the SIP so far has a perfect track record of predicting what each contestant will choose. That is, whenever the contestant has chosen both boxes in the past, it has always turned out that Box B was pre-loaded with no money, and whenever a contestant chose box B only, it was always found to contain $1 million.

    So, vote. What would you choose?

    And, more importantly, explain why you'd make the choice you made.
     
    Last edited: Jan 25, 2017
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  3. rpenner Fully Wired Staff Member

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    On physical principles, I don't believe such a SIP is possible, but likewise, it's always possible to have a good track record.

    The payoff matrix of this game seems to be:
    \(\begin{array}{c|c|c} \backslash & \textrm{SIP correct} & \textrm{SIP incorrect} \\ \hline \\ \textrm{take box B} & 10^6 & 0 \\ \hline \\ \textrm{take both} & 10^3 & 1.001 \times 10^6 \end{array}\)
    where if the SIP probability of being wrong (q) is independent of our strategy reduces to:
    \(\begin{array}{c|c} \backslash & \textrm{SIP correct} (1-q) \, + \, \textrm{SIP incorrect} \, q \\ \hline \\ \textrm{take box B} & 10^6 ( 1 - q ) \\ \hline \\ \textrm{take both} & 10^3 + 10^6 q \end{array}\)
    Which says the best pure strategy is to take just box B if \(q < 0.4995\).
    If we assume we can't know q (because, we believe without modeling the SIP that past results are not indicative of future results, then our optimal strategy is to choose between strategies randomly with equal weight, with a statical average outcome of USD 500,500 independent of q. However, the variance (if q is far from 0.4995) is so large, would you second-guess the coin toss?

    The momentary fame I would get if I picked box B alone and I were to be the first contestant to find it empty would exceed the marginal value of an extra $1000, so I'm probably the type of person who would choose box B alone. The million dollars will be my consolidation prize for not being part of history.
     
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  5. Sarkus Hippomonstrosesquippedalo phobe Valued Senior Member

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    Unless I have misunderstood the dilemma, I'd take box B only, and I'm fairly sure the predictor would predict correctly.
    By considering whether or not to go for box A as well one is really deciding whether to gamble $1m for the chance of winning just an extra $1k.
    The reward just isn't there for the risk you're taking.
    Zero risk and you walk away with $1m, but take both and at most you can get $1.001m.

    There is no dilemma or paradox here for me.... I'd always just take box B.
     
    Last edited by a moderator: Jan 26, 2017
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  7. C C Consular Corps - "the backbone of diplomacy" Valued Senior Member

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    Perfect track record for years means one is literally going against the potency of a fantasy being, despite whatever claim of the SIP accomplishments being nothing more than information-gathering, calculative and evaluative procedures. No sign of even a random impulse or whim to fail deliberately, either. Thus hopeless.

    During that span the array of personality types and their assorted tactical thinking would largely have been exhausted; thereby plenty of individuals have already chosen B alone. Thus no post-game benefits to be had from uniqueness of choice.

    So even without the immediate, desperate few hundred dollars need of a homeless person or somebody being chased by the thugs of Lennie the loan shark, I might as well choose the one grand. Since otherwise walking away with zero benefits is pretty much guaranteed (any local business that might hire me for a commercial just for the trivial celebrity stratus of participating in the show would still do so anyway).
     
    Last edited: Jan 25, 2017
  8. DaveC426913 Valued Senior Member

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    5,643
    Others seem to have mirrored the same thought I had as I was reading.

    The dilemma is predicated on the existence of a device that can read the future (even if the explanation is a rationalization of how it might do that.)

    I thnk that's a non-trivial condition of the thought experiment.

    So, it seems to me, it boils down to whether I believe such as device is possible.
     
  9. James R Just this guy, you know? Staff Member

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    A couple of people have commented on the impossibility of a perfect predictor.

    It's actually unnecessary to the problem that the SIP be perfect. Suppose, for example, that the SIP was only correct 80% of the time. Would that change your mind?
     
  10. James R Just this guy, you know? Staff Member

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    Here's an argument for taking both boxes:

    The boxes are pre-loaded before you make your choice. By the time you make the choice, the SIP has already left the building. So, Box B either contains zero or $1 million. Your choice now can't affect what happened in the past (i.e. at the time the boxes were loaded). So, what have you got to lose by taking both boxes?

    If Box B contains $1 million and you take both, you walk away with $1,001,000, whereas if you take only box B, you miss out on that 'extra' thousand.

    On the other hand, if Box B contains nothing and you choose both then you end up with $1000, whereas you end up with nothing by choosing Box B alone.

    Either way, you're better off by $1000 if you take both boxes.
     
  11. C C Consular Corps - "the backbone of diplomacy" Valued Senior Member

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    1,759
    In the haste of reading and responding during a brief morning break and confusing the extra factors of the original thought experiment with the version in the OP of this thread, I didn't grok it correctly to begin with, anyway.

    A contestant should always select box-B alone if the SIP is straightforwardly going to place the million dollars in it as the result of that prediction rather than responding with the opposite of leaving it empty. The former makes so little sense (in terms of any game show which does not desire to continuously pay out so massively) that my visual cognition flipped the words meaning-wise. One would want the SIP to be perfect in its predictions.
     
    Last edited: Jan 26, 2017
  12. iceaura Valued Senior Member

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    23,216
    Variation on #7

    There is no way to actually get the million, if the SIP is perfect.

    So take the thousand, and if the SIP is imperfect you get the million too.

    Nope. Not if the error was random, anyway - so it was as likely to have left a mistake million as a mistake empty. That just boosts your odds of getting the million.
     
    Last edited: Jan 26, 2017
  13. James R Just this guy, you know? Staff Member

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    Huh?

    If you choose Box B only, you get $1 million, as long as the SIP predicted you would choose Box B only.

    Are you sure you've got the scenario straight? The choice is not both boxes or just box A; it's both boxes or just box B.
     
  14. iceaura Valued Senior Member

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    23,216
    You are absolutely correct, I misread the problem - and the correct reading, followed by the same reasoning, takes box B without hesitation. That is, don't bet 999k the SIP was wrong.

    In that one, though, the odds matter: at some level of random error, at some odds that choosing box B gives you nothing while choosing both gets you the million anyway, you pick both. The exact odds would depend on how much you needed a thousand dollars at the moment - there are circumstances wherein the difference between a thousand dollars and nothing is bigger than the difference between a thousand and even a certain million.
     
  15. James R Just this guy, you know? Staff Member

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    What do you think of the argument in post #7?
     
  16. James R Just this guy, you know? Staff Member

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    From my (admittedly limited) reading on the internet about this, the "right" thing to do in this scenario is a question that is still debated among philosophers.

    As for the general public, most people when asked say the right course of action is obvious. But one course of action is obviously right for about half the population, and the other is obviously right for the other half!
     
  17. RajeshTrivedi Valued Senior Member

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    1,340
    is it really a paradox? I feel it depends on participant's present financial standing, his present need and of course greed (this one surely is an individual characteristics).

    Once the Boxes are brought Forward
    A. If A is blank, then there is no point taking A+B, just B will do.
    B. If A contains 1000, then if the participant is in dire need of around $1000, if it is the matter of life and death for him (great need), then he will choose A+B.
    C. If A contains 1000, and particpant is just of ordinary means with some greed, then he will choose A+B.
    D. If A contains 1000, few people even of ordinary means may go for B only, just knowing about SIP.
    E. People very sound fiancial mostly will go for B.

    In front of SIP, knowing that particpants know about SIP methodology.

    1. Rich people will answer only B not A+B, if the question is put to them.
    2. Not so rich people will try to fool SIP, assuming that SIP can be fooled. Idea is to convey to SIP that particpant will take B only.

    Conclusion.
    1. Rich guys will win $1m, as usual money fetches money.
    2. Needy will most likely get $1000 if A contains that.
    3. The dilemma of ordinary means but simple guys will be sensed by SIP, they wont get 1m.
    4. Smartass who could fool SIP, may get 1m.

    Is it really half half ?
     
    Last edited by a moderator: Jan 26, 2017
  18. iceaura Valued Senior Member

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    I think it's something SIP would have had to include in its predictions, to be perfect.
    That is, your reasoning now was part of SIP's prediction then, just as all the others were that SIP got right.

    So you are betting on whether SIP ever errs. And it's a bad bet, by the track record.
     
  19. Sarkus Hippomonstrosesquippedalo phobe Valued Senior Member

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    If you honestly think so, and if the SIP basis its decision on you honestly thinking so, then you should take both boxes and walk away with USD 1,000.
    For the rest of us, we'll happily walk away with the USD 1 million by believing that this will yield the best result.

    The flaw in the argument you put forth, as I see it, is that it assumes that what is in box B is somehow random. But it's not. If one assumes it is an accurate predictor (and indications are that it is) then the options of payout are only USD 1,000 (if you take both boxes) or USD 1,000,000 (if you take just the one). There is no chance of getting USD 1,001,000 - if one assumes the SIP is always accurate.
    The maths is rather simple on who is better off.

    Hint: it's not the person who takes 2 boxes.

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    It doesn't matter if you rationalise your decision before or after the game, as the SIP is assumed an accurate predictor: it already knows what your decision will be - and has so far always been right. You can not second-guess yourself as the SIP would already have taken your second-guessing into account. Whatever you pick, it knew what you would pick.
     
  20. James R Just this guy, you know? Staff Member

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    RajeshTrivedi:

    I don't see how it matters whether you are rich or poor to start with. The question is whether you can make a reasoned choice to take just box B or both boxes.

    Your reasoning seems to be something along the lines of "I can't risk getting nothing, so I have to take two both boxes." But given the track record of the SIP, that would mean that you'd likely end up with $1000, when you could have had $1 million. Have you made a rational choice, then?
     
  21. James R Just this guy, you know? Staff Member

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    Sarkus:

    The main reason for the argument in post #7, as far as I can tell, is that your choice now can't affect what was put in box B (or not put there) some time ago. There can't be reverse causation.

    To make this more vivid, imagine your significant other is sitting on the other side of the table where the boxes are, and on that side of the table both boxes are transparent. So, as you contemplate your choice, this other person is looking at the two boxes - box A with $1000 inside, and box B with whatever it contains, right now.

    What would that person want you to do, right now? Take just box B, or both boxes?
     
  22. iceaura Valued Senior Member

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    23,216
    But there wasn't. There was prediction. And that entire argument, just as you are having it with yourself and all those others had with themselves, would have been part of said prediction, which by presumption has not missed yet. It was your behavior, including your choice and all the arguments behind it, that was predicted.

    Correct predictions do not reverse causation.
    Regardless of what they want, they know what you are going to do - because they can see the prediction.
     
  23. RajeshTrivedi Valued Senior Member

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    1,340
    A. For a rich guy is below not a reasoned choice?

    I dont worry about loose change of 1000, I want only 1m so I will go for B.

    B. For a needy chap is below not a reasoned choice?

    I desperately need 1000, so I will go for A+B if A has 1000.

    C. For a smartass is it not reasoned enough to fool the SIP.

    Since SIP will feed 1m in B if I could fool it that I would choose only B.

    D. For an average chap is it not reasoned enough to think, okay something is better than nothing and I will for A+B.


    Actually SIP can see through B and D, so these guys will not get 1m. So either the rich (A) or crooks (C) will get 1m. Thats what happens in real life. Isn't it?

    (This paradox(?) is nothing but making a mountain out of molehill.)
     

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