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DanielLC 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?
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.