Sysice comments on Simulation argument meets decision theory - Less Wrong Discussion
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Your problem setup contains a contradiction. You said that X and X*_i are identical copies, and then you said that they have different utility functions. This happened because you defined the utility function over the wrong domain; you specified it as (world-history, identity)=>R when it should be (world-history)=>R.
How I interpreted the problem- it's not that identical agents have different utility functions, it's just that different things happen to them. In reality, what's behind the door is behind the door, while in the simulation rewards X* with something else. X* is only unaware of whether or not he's in a simulation before he presses the button- obviously once he actually receives the utility he can tell the difference. Although the fact that nobody else has stated this makes me unsure. OP, can you clarify a little bit more?
Yes, this is how I view the problem as well.