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Comment by aspirin | Hacker News Reader

There is something wery odd about Newcomb’s Problem. If the Predictor can predict my choice with 100% accuracy, it's not really a choice, is it? Free will does not exist in this scenario, and therefore I cannot meaningfully choose between one or both boxes. The question is nonsensical.

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Instead of choosing a box, submit the source code of a program that decides whether or not to open a box. Then, the predictor reads the source code, puts money in boxes, and only then does your source code run and open boxes.

Now, imagine that there was a computer program that makes the same choices you do in the same situations, and the Predictor can read that source code before filling the boxes.

That's the intuition pump I use for thinking about Newcomb-like problems.

I might be mistaken, but it seems to me that the predictor should also be able to solve the halting problem. Additionally, if the entity to which the source-code is a descriptor for is so simple that they can be predicted without full simulation, can we really say they had free will?

The program isn't given infinite time to run so its not a halting problem case.

I guess it boils down to how one defines "choice".

The minimal way to think about choice is to require the existence of an agent that is capable of producing binary outputs. Each output signifies a decision the agent has made. The agent is treated as a black box and whether the agent is deterministic or not remains unspecified and irrelevant.

Another approach is to attempt to endow the agents with some sort of free will.

An interesting realization is that there is no way to know whether humans or anything else for that matter qualify for the second option. There may exist a deity, alien or Matrix root who already knows all our choices before we do.

The funny thing is: we couldn't even tell the difference.

The paradox doesn't go away if you assume that the Predictor is occasionally wrong. In real life, the people who know you best could probably predict your answer to the question with some accuracy better than chance. (For example, maybe your belief in free will biases you toward the two-box answer because you believe that your decision can't be predicted). This is just a thought-experiment that takes that real-life situation to its logical extreme to make the paradox more apparent.

I see it in a similar way and think about it in the following two steps. First convince the predictor that you will either choose AB or B - and he will always predict exactly this - then actually choose either AB or B, but both choices are not necessarily the same. Of the four possibilities you can safely ignore AB-B because it is worse then unproblematic AB-AB. If you want the million you have to convince the predictor that you will choose B and that means you have to either do B-B or B-AB.

But you can only perform B-AB if you manage to fool the predictor and especially you can not do B-AB in a deterministic universe without free will (let's ignore that you don't even have control over the first step in that scenario). B is definitely the right choice in the first step and then changing to AB is the best choice in the second step, but whether you can actually do this depends on your stance on free will and the like.

Also if you include a mixed (randomized) strategies the postulated Newcomb's problem is idiotic, because the other player is not an oracle. That's why they included a dirty fix that "if the Predictor predicts that the player will choose randomly, then box B will contain nothing".

Invoking nondeterminism doesn't make the thought experiment easier, just more complicated. From http://www.scottaaronson.com/blog/?p=30 :

>(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.)

Even if you have "free will" and your actions are semi-random, that's not different than flipping a coin to make your decisions.

The Predictor might know which way you'll choose, but you don't.

It's assuming you'll still experience the perception of having a choice. It predicts your actions but doesn't tell you, how would that be different from choices you're making if you actually did have free will (in both cases you say "I think I have free will" whether or not you do)?

Since you have imperfect information about yourself (this neuron talked to this neuron by these rules) you don't attribute the cause of your own behavior to anything other than "I did that".

I think the example from 1.3 is much more clarifying than the one-box vs two-box problem, there's no "predictor" involved

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