Double-thick transistors and other subjective phenomena

Was this motivated by Nick Bostrom's paper? If not, you might enjoy it--it also discusses the idea of splitting a consciousness into copies by duplicating identical computational processes.

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.

How many anthropic atheists does it take to change a lightbulb?

Is behaviorism the right way to judge experience? Suppose you simply recorded the outcome of the sleeping beauty problem for a computer X, and then replayed the scenario a few times using the cached choice of X instead of actually running X again each time. For that matter, suppose you just accurately predict what X will conclude and never actually run X at all. Does X experience the same thing the same number of times in all these instances? I don't see a behavioral difference between running two thin computers layered on top of each other and using one thin computer and one cached/predicted result.

Another way to ask this is how thin can you slice the computer before it stops having experience? From a behaviorism perspective you can thin it all the way down to just a cached/predicted responses.

If we can't differentiate between how much experience a computer has when it's running thin or thick, then that implies we can't truly measure how much experience a computer has at different times or places. It's just an assumption that a computer now and a computer 5 minutes from now have the same measure of experience, but I don't see a way to test that assumption.

My intuitive guess is that all that matters is if the program is run. It doesn't matter if it's on a double-thick computer, or two computers, or what.

Quantum physics seems to suggest a different result. If you run a computer with twice the wave-form, it has four times the subjective probability. It could be that we got the equation wrong and all the values we're using are the square root of what they should be. It could be that there's discrete universes in there and the wave-form is just the square root of the density. It could be something I haven't thought of. But it could be really unexpected anthropics.

Subjective experience is also valued differently for humans - in some domains. Not all persons are equal in an airplane. You may pay extra if you are heavy - some may take this as unfair not allocating equal weight. Conversely tall and/or heavy people often experience a natural authority that comes with physical presence. Even if their live is consered equally worthy they nonetheless gain some advantage from their stature.

See also Gains from trade: Slug versus Galaxy - how much would I give up to control you?.

What do I claim explains this? The simple fact that you only offer the double computer one bet, not two

What makes you so confident that the double computer's offered one bet and the two separate computers are offered two? Because the two separate computers might make two different choices? Only if there's some other difference (e.g. you've fitted separate random number generators to the two separate computers, and the double computer only has one). Because you're paying out twice as much if you lose? Presumably you put twice as much current into the double computer as to each of the single computers. Because you, as the experimenter, are offering different experiences to the two separate computers? That just repeats the same problem one level higher (considering that there are probably Everett branches in which you took both different actions with the double computer).

You can have same software running on multiple machines. There's still intermediate steps where you go from 1 to 2.

I think the question is fundamentally misguided with regards to the meaning of the word "probability" , and the phenomenalist position is the only correct one. I.e the question is meaningless. The "probability" is not a property of the world of sleeping beauty problem, it's just an intermediate value in the calculations, correctness of which is only defined by it's end use, e.g. in bets. Where the best value depends on which instances of the program we prefer to end up betting wrong.