For instance, accelerating value growth by 10^-5 pp over the next 10 years (e.g. from 7.83 % to 7.83001 %) increases the future expected value (EV) of the world as much as decreasing value extinction risk over the same period by 10^-5 pp (e.g. from 10^-7 to 0).
Say there is a probability r = “value extinction risk” that the future EV drops to 0 in a given period. In addition, say the future EV otherwise becomes (1 + g)*V, where g represents the value growth over the period, and V is the future EV if there is no value growth. The (unconditional) EV is EV_i = r*0 + (1 - r)*(1 + g)*V = V*(1 + g)*(1 - r).
Consider an intervention which changes value growth over the period by Delta_g, and value extinction risk over the period by Delta_r. It changes the future EV to EV_f = V*(1 + g + Delta_g)*(1 - r - Delta_r). So it changes the future EV by Delta_EV = EV_f - EV_i = V*((1 - r)*Delta_g - (1 + g)*Delta_r - Delta_g*Delta_r).
Assume the intervention cost is sufficiently low for Delta_g and Delta_r to be small. I think there is no meaningful loss of generality because interventions can be decomposed into low cost ones. The last term of Delta_EV becomes negligible. So the intervention changes the future EV by V*((1 - r)*Delta_g - (1 + g)*Delta_r). Consequently, accelerating value growth by Delta (from g to g + Delta) increases the future EV by k = (1 - r)/(1 + g) times as much as decreasing value extinction risk by Delta (from r to r - Delta). Note this holds regardless of how the future looks after the period.
Suppose both value growth and value extinction risk over the period are much smaller than 1. I believe there is no meaningful loss of generality for interventions targeting the next 10 years if the human population is a good proxy for value during this period. The human population is expected to grow 7.83 % (= 8.95/8.30 - 1) from 2026 to 2036, and I guess the probability of human extinction over this period is something like 10^-7. In this case, k in the formula above becomes roughly 1. So accelerating value growth over the next 10 years by 10^-5 pp (e.g. from 7.83 % to 7.83001 %) increases the future EV as much as decreasing value extinction risk over the same period by 10^-5 pp (e.g. from 10^-7 to 0). Relatedly, Toby Ord noted that, “if prioritising between an enhancement and existential risk reduction, it all comes down to which one has the higher factor”.
I have little idea about the drivers of the current and future EV. I am very uncertain about how to weight different species and non-biological systems. So I would prioritise decreasing uncertainty about this over supposedly accelerating value growth, or decreasing value extinction risk based on very rough proxies for value like human population.
