I’ve had exactly the same thought before but never got around to writing it up. Thanks for doing it so I don’t have to :-)
There are only so many possible human shaped computations that are valuable to me
I would surmise that value-space is not so much “finite in size” but rather that it fades off into the distance in such a way that it has a finite sum over the infinite space. This is because other minds are valuable to me insofar as they can do superrationality/FDT/etc. with me. In fact, this is the same fading-out function as in the “perturb the simulation” scenario; i.e.:
:= The value that places on a world where and both exist
:= The value that places on a world where exists but doesn’t
:= The value that places on a world where doesn’t exist but does
Claim:
However, the main problem with this perspective is what to do with quantum many-worlds. Does this imply that “quantum suicide” is rational, e.g. that you should buy a lottery ticket and set up a machine that kills you if you don’t win? This is bullet I don’t want to bite (so to speak...)
The OP isn’t making any claim like this; the question isn’t whether any particular experience has value in-and-of-itself, but is only making a claim about the correct way to evaluate the total utility in a world with multiple experience.
By analogy, consider special relativity: If a train is moving at 0.75c relative to the ground, and a passenger on the train throws a ball forward at 0.5c, then that means the ball is moving at 0.91c relative to the ground. But there is no reference frame in which the ball is “really” moving at 0.16c.
Or, more pertinently, suppose we have two identical simulations playing out at the same time. Each one contributes zero marginal utility to a world in which the other one exists (and might be told this by Omega), but that doesn’t mean that the two of them together have zero utility.