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#1 2016-04-30 22:59:31

Relentless
Member
Registered: 2015-12-15
Posts: 624

Two boxes

Hi everyone!

What do you think of the famous Newcomb's paradox?

The player is presented with two boxes and, wishing only to maximise the amount of money he receives, may take both boxes or only box A. Box B contains $1k. Already it seems clear that taking both boxes is dominant; however, at least for most, it is about to become less clear. Before the decision is made, a brain-scanner with a demonstrated near-perfect accuracy predicts the decision. If it predicts that the player will choose only box A, box A contains $1m. Otherwise, it is empty.

Which would you choose? (:

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#2 2016-05-01 03:54:29

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Two boxes

Is it a fiction?


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#3 2016-05-01 04:50:31

Relentless
Member
Registered: 2015-12-15
Posts: 624

Re: Two boxes

Yes, it is a very divisive hypothetical. I think it could still be controversial with a fallible human predictor, however.

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#4 2016-05-01 17:35:13

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Two boxes

It is not clear whose brain is scanned and what is the result? What is the probability that the prediction can go wrong?Is the predictor independent or is associated with manipulating the contents of the box?


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#5 2016-05-01 20:14:53

Relentless
Member
Registered: 2015-12-15
Posts: 624

Re: Two boxes

Suppose your brain is scanned; is it correct to one-box or two-box? The probability of the prediction going wrong is close to zero in this example (although I think the problem persists whenever the probability is below 49.5%). The predictor chooses, based on the prediction, what is in the box (for the sake of argument, say the prediction occurs before the boxes are presented to you). A million dollars if it predicts you will take one box, and nothing if it predicts you will take both.

Shall I explain the intuitions of those arriving at either answer to make clear what is so difficult?

Last edited by Relentless (2016-05-01 20:20:32)

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#6 2016-05-04 08:11:39

Relentless
Member
Registered: 2015-12-15
Posts: 624

Re: Two boxes

My answer:

The paramount ambiguity in the paradox is whether the content of box A is, or is not, somehow dependent on the decision. It appears to many not to be because in fact there cannot be a physical causation. Those with this view are content to assert that taking box B as well will yield strictly $1k more than not doing so, irrespective of the prediction. However, the contention here is that this view is in error due to an overlooked inference. While the decision does not cause the content of the box, the prediction does; and the prediction is thoroughly correlated with the decision. Although the decision does not cause the prediction, the prediction (and hence the content of the box) can be inferred from the decision. Therefore, the content does indirectly depend on the decision. Those who intuit that the content of the box is fixed may be answered: Yes, but only in the sense that the decision is fixed; for the one invariably corresponds to the other. (Incidentally, if the expectation of the choices are modelled as functions of the accuracy of the predictor, it is determined that, due to the high stakes, for box A alone to be preferred the predictor need only be more than 50.5% accurate. Box A alone is potentially a winning strategy even with an ordinary human predictor!)

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