Did you see there's a section in the post about negative value? It does discuss the first point you raised, that our intuitions about variety suffering aren't as clear-cut, and that it's not so obvious how we'd ideally handle these cases:
I at least personally get the intuition that a variety of bads makes an outcome worse. [...] My intuition is that Diverse Hell is worse than Uniform Hell, but I accept that the intuition here is less clear than it is in the positive case.
I'm not sure if this would just create other technical problems I haven't thought of, but one solution could just be to replace "best possible" with, e.g., "ex ante 99.9th percentile". Then you wouldn't have this discontinuity from changing the max, but it captures basically the same intuition?
(One problem is that it's not obvious what the threshold should be. But my guess is that when people are trying to figure out the relevant denominator for PVBPF they're usually implicitly truncating the probability distribution over outcomes somewhere anyway, since it seems very hard to reason about the absolute maximum.)
Claude also suggested something like a conditional expectation of the upper tail, e.g. E[V|V≥q0.999], which seems interesting but I've not thought carefully about.
Did you see there's a section in the post about negative value? It does discuss the first point you raised, that our intuitions about variety suffering aren't as clear-cut, and that it's not so obvious how we'd ideally handle these cases:
I'm not sure if this would just create other technical problems I haven't thought of, but one solution could just be to replace "best possible" with, e.g., "ex ante 99.9th percentile". Then you wouldn't have this discontinuity from changing the max, but it captures basically the same intuition?
(One problem is that it's not obvious what the threshold should be. But my guess is that when people are trying to figure out the relevant denominator for PVBPF they're usually implicitly truncating the probability distribution over outcomes somewhere anyway, since it seems very hard to reason about the absolute maximum.)
Claude also suggested something like a conditional expectation of the upper tail, e.g. E[V|V≥q0.999], which seems interesting but I've not thought carefully about.