Newcomb's problem splits people 50/50 in two camps, but the interesting thing is that both sides think the answer is obvious, and both sides think the other side is being silly. When I created a video criticizing Veritasium's video This Paradox Splits Smart People 50/50 I received a ton of feedback particularly from the two-box camp and I simply could not convince anyone of why they were wrong.
That lead me to believe there must be some cognitive trap at play: someone must be not seeing something clearly. After a ton of debates, reading the literature, considering similar problems, discussing with LLMs, and just thinking deeply, I believe the core of the problem is recursive thinking.
Some people are fluent in recursivity, and for them certain kind of problems are obvious, but not everyone thinks the same way.
My essay touches Newcomb's problem, but the real focus is on why some people are predisposed to a certain choice, and I contend free will, determinism, and the sense of self, all affect Newcomb's problem and recursivity fluency predisposes certain views, in particular a proper understanding of embedded agency must predispose a particular (correct) choice.
I do not see how any of this is not obvious, but that's part of the problem, because that's likely due to my prior commitments not being the same as the ones of people who pick two-boxes. But I would like to hear if any two-boxer can point out any flaw in my reasoning.
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Notes -
My interpretation:
Free will is indistinguishable from randomness, and your brain has some randomness. The alien understands your personality, but can't predict randomness. For example, maybe immediately before the experiment, they cloned you and ran a perceptually identical experiment; then, if your clone picked both boxes in the practice run, the alien didn’t fill the opaque box for the real run.
You can win $1,001,000, but only if you're lucky. For example, let's say you have a 50% chance of choosing both boxes. Then the alien has a 50% chance of filling the opaque box. You have a 25% chance of winning $1,001,000...but a 25% chance of winning $0, and 25% chance of winning $1,000.
You can't trick the alien: if you're more likely to choose both boxes, the alien is less likely to fill the opaque box. Formally, if you with probability p pick both boxes, the alien with probability 1 - p fills the opaque box. Imagine your clone, in the same perceived surroundings, with your same strategy.
If the experiment was repeated ∞ times, on average you'd win $1000p^2 + $1000000(1 - p)^2 + $1001000p(1 - p) = $1000000 - $999000p; increasing p strictly decreases your average win. The statistically optimal strategy is to always pick one box.
No. You are forgetting the correlation. The problem very clearly states that the predictor "almost certainly" will predict your choice. That means that for the 50% that you choose one-box, the predictor won't be filling the mystery box 99.99% of the time. And for the 50% that you chose one-box, the predictor will be filling the mystery box 99.99% of the time.
So the breakdown is: $1,001,000 (0.005%), $1,000,000 (49.995%), $1,000 (49.995%), $0 (0.005%).
That isn't quire right because the predictor is not 100% accurate. If we assume the accuracy is 99.99% (q), then the probability that the predictor will fill the mystery box is (q)(1 - q). Close, but not quite the same.
Correct.
But the real question my essay is trying to explore is why some people do not see that's the case. In my experience the reason why people choose two-boxes is that they completely ignore the accuracy of the predictor, and instead of assuming that q is close to 100%, they simply treat it as a completely unknown variable that could take any value, including 0.01, despite the formulation of the problem.
Why do they do that?
You’re right, I misunderstood the problem.
Why do people gamble?
Alternatively, they also misunderstand the problem. I wonder if the “practice run” method of predicting their behavior would change their mind.
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