It’s true there are other scenarios that would recover infinite value. And the proof fails, as mentioned in the convergence section, with changes like r∞=0, or when the logistic cap c→∞ and we end up in the exponential case.
All that said, it is plausible that the universe has a finite length after all, which would provide that finite upper bound. Heat death, proton decay or even just the amount of accessible matter could provide physical limits. It’d be great to see more discussions on this informed by updated astrophysical theories.
Personally, I do not think allowing the risk to decay to 0 is problematic. For a sufficiently long timeframe, there will be evidential symmetry between the risk profiles of any 2 actions (e.g. maybe everything that is bound together will dissolve), so the expected value of mitigation will eventually reach 0. As a result, the expected cumulative value of mitigation always converges.
It’s true there are other scenarios that would recover infinite value. And the proof fails, as mentioned in the convergence section, with changes like r∞=0, or when the logistic cap c→∞ and we end up in the exponential case.
All that said, it is plausible that the universe has a finite length after all, which would provide that finite upper bound. Heat death, proton decay or even just the amount of accessible matter could provide physical limits. It’d be great to see more discussions on this informed by updated astrophysical theories.
Thanks for following up!
Personally, I do not think allowing the risk to decay to 0 is problematic. For a sufficiently long timeframe, there will be evidential symmetry between the risk profiles of any 2 actions (e.g. maybe everything that is bound together will dissolve), so the expected value of mitigation will eventually reach 0. As a result, the expected cumulative value of mitigation always converges.