That aside, I do have an object-level comment. Nick states (in section 6.3.1) that Period Independence is incompatible with bounded utility function, but I think that’s wrong. Consider a total utilitarian who exponentially discounts each person-stage according to their distance from some chosen space-time event. Then the utility function is both bounded (assuming the undiscounted utility for each person-stage is bounded) and satisfies Period Independence.
I agree with this. I think I was implicitly assuming some additional premises, particularly Temporal Impartiality. I believe that bounded utility + Temporal Impartiality is inconsistent with bounded utility. (Even saying this implicitly assumes other stuff, like transitive rankings, etc., though I agree that Temporal Impartiality is much more substantive.)
Another idea for a bounded utility function satisfying Period Independence, which I previously suggested on LW and was originally motivated by multiverse-related considerations, is to discount or bound the utility assigned to each person-stage by their algorithmic probability.
I am having a hard time parsing this. Could you explain where the following argument breaks down?
Let A(n,X) be a world in which there are n periods of quality X.
The value of what happens during a period is a function of what happens during that period, and not a function of what happens in other periods.
If the above premise is true, then there exists a positive period quality X such that, for any n, A(n,X) is a possible world.
Assuming Period Independence and Temporal Impartiality, as n approaches infinity, the value of A(n,X) approaches infinity.
Therefore, Period Independence and Temporal Impartiality imply an unbounded utility function.
The first premise here is something I articulate in Section 3.2, but may not be totally clear given the informal statement of Period Independence that I run with.
Let me note that one thing about your proposal confuses me, and could potentially be related to why I don’t see which step of the above argument you deny. I primarily think of probability as a property of possible worlds, rather than individuals. Perhaps you are thinking of probability as a property of centered possible worlds? Is your proposal that the goodness of a world A with is of the form:
g(A) = well-being of person 1 prior centered world probability of person 1 in world A + well-being of person 2 prior centered world probability of person 2 in A + …
? If it is, this is a proposal I have not thought about and would be interested in hearing more about its merits and why it is bounded.
OK, I”ll ask Paul or Stewart next time I see them.
Does your proposal also violate #1 because the simplicity of an observer-situated-in-a-world is a holistic property of the the observer-situated-in-a-world rather than a local one?