The only probability I can really compute here is the probability of getting lucky 100 times straight: 2^{-100}. But I think (1) is really unlikely also, and I believe that (3) is possible. So, I think it’s most likely to be case (3). So, I’ll pick one box.

]]>Blake: You don’t save yourself any work that way. If you go and compute the answer before picking boxes, then you’ll know the answer, but you could do that just as well without any Predictor involved. It doesn’t even make you particularly hard to predict (no superhuman resources required on the part of the Predictor, other than knowing which problem you’ll use). If you don’t compute the answer but rather depend on the Predictor to tell you, then the Predictor doesn’t have to compute the answer either, it can use the same algorithm you did to actually pick boxes.

]]>I like that idea of using some astronomical event. Then the predictor may have to simulate the whole universe.

For a different kind of fun, you could base your decision on some mathematical result, one which is in principle knowable but which you don’t know. “If the third digit in the exponent specifying the fiftieth Mersenne prime is even, I will choose both boxes.”

]]>I’m not sure you’d need a copy of the predictor. The problem stipulates that the predictor simulated you prior to you showing up to make your decision. I just make simulating me as difficult as solving the halting problem.

So that leaves several possibilities:

#1 In a certain % of worlds the Predictor never halts and thus never offers me the opportunity.(This means I never have to run non-halting programs, because I never reach the point where *I* have to make a decision)

#2 The Newcomb problem has a hidden stipulation that I always pick halting strings.

That would put me in a very strange situation if I actually get an opportunity to make a decision. I’m picking out of a box of “random” programs, and no matter which string I pick, I happen to pick a halting program. I know this, because if I had picked a non-halting program, the simulation wouldn’t have halted and I wouldn’t be granted the opportunity to choose.

So If I set the intentionality right now, that I’m going to test a program to see if it halting, then I can guarantee that if I ever find a predictor, then I’ll not only have a means of winning $1M, but also an oracle for the halting problem. I’m not even cheating. A rational actor would prefer $1M and an oracle, over $1M alone.

]]>Your argument that it matters whether the clone gets punished for pushing the button, depends on the assumption that the clone *can* act differently from the original Dr. Evil. My intuition was that, *because* they’re perfect clones, they both necessarily make the same choice—in which case superrationality becomes no different from ordinary rationality, and the argument against pushing the button goes through. Only if Dr. Evil and his clone physically *can* act differently, do we have to assume either that the clone will be punished for pushing the button, that they’re superrational, or that the original Dr. Evil cares about the clone.