It’s quite likely the extinction/existential catastrophe rate approaches zero within a few centuries if civilization survives, because:
Riches and technology make us comprehensively immune to natural disasters.
Cheap ubiquitous detection, barriers, and sterilization make civilization immune to biothreats
Advanced tech makes neutral parties immune to the effects of nuclear winter.
Local cheap production makes for small supply chains that can regrow from disruption as industry becomes more like information goods.
Space colonization creates robustness against local disruption.
Aligned AI blocks threats from misaligned AI (and many other things).
Advanced technology enables stable policies (e.g. the same AI police systems enforce treaties banning WMD war for billions of years), and the world is likely to wind up in some stable situation (bouncing around until it does).
If we’re more than 50% likely to get to that kind of robust state, which I think is true, and I believe Toby does as well, then the life expectancy of civilization is very long, almost as long on a log scale as with 100%.
Your argument depends on 99%+++ credence that such safe stable states won’t be attained, which is doubtful for 50% credence, and quite implausible at that level. A classic paper by the climate economist Martin Weitzman shows that the average discount rate over long periods is set by the lowest plausible rate (as the possibilities of high rates drop out after a short period and you get a constant factor penalty for the probability of low discount rates, not exponential decay).
Crossposting Carl Shulman’s comment on a recent post ‘The discount rate is not zero’, which is relevant here: