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AABoyles comments on Simulation argument meets decision theory - Less Wrong
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Either I'm missing something or it isn't interesting. If you aren't a Sim, you get 1 for Sim and .9 for not Sim. So your best play is Sim. If you are a Sim, you get .2 for Sim and .1 for not Sim, so your best play is Sim. Regardless of the piece of information you lack, your best play is Sim.
The question is whether this is analogous to Newcomb's problem. After all, one can make the same argument you make that "no matter what the contents of the box, taking both boxes is the dominant strategy,"
I agree. It seems to me that the speciality of the Necomb Problem is that actions "influence" states and that this is the reason why the dominance principle alone isn't giving the right answer. The same applies to this game. Your action (sim or not sim) determines the probability of which agent you have been all along and therefore "influences" the states of the game, whether you are X or X*. Many people dislike this use of the word "influence" but I think there are some good reasons in favour of a broader use of it (eg. quantum entanglement).
Actually, when working through it, it looks like pre-nap self was wrong! (Okay no distancing, I was wrong :P). I still wrote up a big comment though, you'll see what I neglected before.
Short counterargument - if rather than a mild reward, the simulated copies got a horrible punishment, would that change whether you picked Sim when you might be one of those copies? Then because of how utility works the simulated copies always matter.
Actually, upon consideration, I will endorse answering "Sim." Will explain in a top level comment after nap. But I certainly agree that the resemblance to Newcomb's problem is why this is interesting.
EDIT: Whoops, I was wrong.
Thanks for pointing this out. I (clearly) missed the thinly veiled Newcomb-likeness of this puzzle.
It is analogous if and only if anthropic utility is coherent and reasonable.
If you decide not to press "sim", you know that there are no simulations. It's impossible for there to be an original who presses "sim" only for the simulations to make different decisions. You're the original and will leave with 0.9.
If you decide to press "sim", you know that there are 1000 simulations. You've only got a 1 in 1001 chance of being the original. Your expected utility for pressing the button is slightly more than 0.2.
Oh! I got it. Thanks for patiently sticking this out with me!