I could change the rules and decide not to stand for such tricks (mixed strategies) either. EDIT: No, I couldn’t.
And on the other hand, Omega could deal with mixed strategies perfectly well, and I don’t really understand why people make it so that he explicitly doesn’t tolerate mixed strategies in their problems. For example, in Newcomb’s Problem, if you one-box with probability p, Omega can just fill box B with probability p—for example if p=0.5 your expected winnings in Newcomb’s Problem are $500,500.
In the traditional formulation of Newcomb’s Problem (at least here on Less Wrong), if Omega predicts you’ll use a randomizer, it will leave box B empty.
That’s weird. Assuming human decision making is caused by neural processes, which aren’t perfectly reliable, there’d be no way for a human to not use a randomizer.
Omega could deal with mixed strategies perfectly well, and I don’t really understand why people make it so that he explicitly doesn’t tolerate mixed strategies in their problems.
Use of a mixed strategy might tarnish Omega’s reputation.
I could change the rules and decide not to stand for such tricks (mixed strategies) either. EDIT: No, I couldn’t.
And on the other hand, Omega could deal with mixed strategies perfectly well, and I don’t really understand why people make it so that he explicitly doesn’t tolerate mixed strategies in their problems. For example, in Newcomb’s Problem, if you one-box with probability p, Omega can just fill box B with probability p—for example if p=0.5 your expected winnings in Newcomb’s Problem are $500,500.
That sounds tricky—unless you are a mind-reading superintelligence!
Yeah, you’re right. I can’t decide to not stand for mixed strategies, only Omega can.
In the traditional formulation of Newcomb’s Problem (at least here on Less Wrong), if Omega predicts you’ll use a randomizer, it will leave box B empty.
That’s weird. Assuming human decision making is caused by neural processes, which aren’t perfectly reliable, there’d be no way for a human to not use a randomizer.
We assume that Omega is powerful enough to simulate your brain and the environment precisely, and that quantumness is negligible.
In that case, you could still say that there’s no way not to use a randomizer, but Omega would be using the same randomizer with the same seed.
If you use flipping a coin as a randomizer, Omega could simulate that too. But traditionally using coins doesn’t fly while using brains is okay.
Use of a mixed strategy might tarnish Omega’s reputation.