The passage you quoted was just an example, I don’t actually think we should use exponential discounting. The thesis of the essay can still be true when using a declining hazard rate.
If you accept Toby Ord’s numbers of a 1⁄6 x-risk this century and a 1⁄6 x-risk in all future centuries, then it’s almost certainly more cost-effective to reduce x-risk this century. But suppose we use different numbers. For example, say 10% chance this century and 90% chance in all future centuries. Also suppose short-term x-risk reduction efforts only help this century, while longtermist institutional reform helps in all future centuries. Under these conditions, it seems likely that marginal work on longtermist institutional reform is more cost-effective. (I don’t actually think these conditions are very likely to be true.)
(Aside: Any assumption of fixed <100% chance of existential catastrophe runs into the problem that now the EV of the future is infinite. As far as I know, we haven’t figured out any good way to compare infinite futures. So even though it’s intuitively plausible, we don’t know if we can actually say that an 89% chance of extinction is preferable to a 90% chance (maybe limit-discounted utilitarianism can say so). This is not to say we shouldn’t assume a <100% chance, just that if we do so, we run into some serious unsolved problems.)
The passage you quoted was just an example, I don’t actually think we should use exponential discounting. The thesis of the essay can still be true when using a declining hazard rate.
If you accept Toby Ord’s numbers of a 1⁄6 x-risk this century and a 1⁄6 x-risk in all future centuries, then it’s almost certainly more cost-effective to reduce x-risk this century. But suppose we use different numbers. For example, say 10% chance this century and 90% chance in all future centuries. Also suppose short-term x-risk reduction efforts only help this century, while longtermist institutional reform helps in all future centuries. Under these conditions, it seems likely that marginal work on longtermist institutional reform is more cost-effective. (I don’t actually think these conditions are very likely to be true.)
(Aside: Any assumption of fixed <100% chance of existential catastrophe runs into the problem that now the EV of the future is infinite. As far as I know, we haven’t figured out any good way to compare infinite futures. So even though it’s intuitively plausible, we don’t know if we can actually say that an 89% chance of extinction is preferable to a 90% chance (maybe limit-discounted utilitarianism can say so). This is not to say we shouldn’t assume a <100% chance, just that if we do so, we run into some serious unsolved problems.)