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gyokuro comments on Open Thread, December 16-31, 2012 - Less Wrong
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About Newcomb's problem + something non-deterministic:
If the contents of box B are increased so that B > A, it seems like by basing the choice of one-boxing or two-boxing off of a quantum coin toss, one could limit Omega's predicting powers from 100% accuracy to a mere coin toss with 50% accuracy.
Where A has $1000 and B has $2000, the average payoff would be $1500 the coin toss ($0 or $3000) versus $1000 by one-boxing and $0 by two-boxing in a way Omega can predict.
Has something like this been considered as a possible resolution?
If you believe in MWI, both outcomes happen, though in different worlds, and Omega knows about both worlds, and stuffs the boxes accordingly.
That's a slightly different problem. How would it be a resolution to the original problem?
Yeah, It wouldn't be a way to win, since in the original problem you could throw a coin and base your decision on that. Average gain of $500,500 isn't so bad, but not nearly as good as $1,000,000 from one-boxing. You're right, it's not a resolution to the paradox, but if the situation is changed it's a possible way of winning.
I guess I'm looking for ways to beat Omega, and I'm trying to figure out if this would be one of them. Something like "harnessing the power of random"?
It's called a mixed strategy Nash equilibrium. It's a very interesting topic on its own, but it doesn't have a whole lot to do with the decision theory paradoxes that Omega is used to show off.
Is it possible for Omega to develop a response to mixed strategies such that the original problem remains, pretty much unchanged?
I can't cite sources off-hand but this suggestion is reasonably standard but taken to be a bit of a cheat (it dodges the difficult question). For this reason it is often stipulated that no objective chance device is available to the agent or that the predictor does something truly terrible if the agent decides by such a device (perhaps takes back all the money in the boxes and the money in the agent's bank account).
Usually, it's just "choosing using a randomizing device will be treated the same as two-boxing."
In other words, the question becomes one of "Omega has two boxes box A and box B, which it fills based on what it thinks you will do. Box A has $1000 and box B has either $0 or $1000000 depending on whether Omega predicts you will take both boxes or only box B, respectively. If Omega predicts that you will do your best to be unpredictable, it will do something bad to you. Should you take box A, box B, or try to be unpredictable?" That question doesn't seem as interesting.