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 Ordnoted 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.
Accelerating value growth is as valuable per percentage point as decreasing value extinction risk, whatever the future looks like
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.