Consider the Sleeping Beauty problem with these computers—in the classic version, our person is asked to give their probability that they’re in the possibility where there’s one thin computer, or the world where there are two thin computers. The correct betting strategy is to bet as if you think the probability that there are two computers is 2⁄3 - weighting each computer equally.
Now, consider altering the experiment so that either there’s one thin computer, or one double computer. We have two possibilities—either the correct betting probability is 1⁄2 and the computers seem to have equal “experience”, or we bite the bullet and say that the correct betting probability is 2⁄3 for a double computer, 10⁄11 for a 10x thicker computer, 1000/1001 for a 1000x thicker computer, etc.
I think what’s happening here is you’re conflating different kinds of stakes in the betting game.
Will the computers be split apart at any point in the future? If so, will the reward stay with one of them, be divided between them, or will they each retain a separate instance the full reward?
In the case of money, clearly it is external to them. So they will have to divide it up somehow, if they split into multiple thin computers in the future—the utility is first divided by the thickness, restoring balance.
On the other hand, if you were giving them an ebook, say, or they were in a simulated environment and the reward was also within the environment (analogous to the many-worlds hypothesis), then yes, those odds are correct, since they can literally receive that many more rewards if they are the thick computer.
I think what’s happening here is you’re conflating different kinds of stakes in the betting game.
Will the computers be split apart at any point in the future? If so, will the reward stay with one of them, be divided between them, or will they each retain a separate instance the full reward?
In the case of money, clearly it is external to them. So they will have to divide it up somehow, if they split into multiple thin computers in the future—the utility is first divided by the thickness, restoring balance.
On the other hand, if you were giving them an ebook, say, or they were in a simulated environment and the reward was also within the environment (analogous to the many-worlds hypothesis), then yes, those odds are correct, since they can literally receive that many more rewards if they are the thick computer.