This looks logarithmic. Plotting the probability over Log(Year − 2022) does look linear (although clearly it is’t, as it is bounded to [0,1], so a better fit would probably be something “arctan”y):
Also, it makes sense to me that uncertainty over “time until E” would behave more like a log-normal distribution (when the probability is fixed). That is, I’d expect that a forecaster’s estimate for years-until-AGI in particular probability p would itself be a lognormal distribution over the years (as I imagine the forecaster would be equally likely to be wrong by twice as many years or half as many years).
This justifies taking the geometric mean over the years (as it corresponds to an average over the log of the years), but not when looking at the probabilities.
Fitting the curve with a linear function (excluding the N/As), we get P(AGI at year y)=log(y−2022)/2−0.15
For y=2030, we’d get p=0.3
For y=2050, we’d get p=0.57
For y=2100, we’d get p=0.79
Or, for a probability p, we’d get the year y=102(p+0.15)+2022.
Plotting the estimates, we get:
This looks logarithmic. Plotting the probability over Log(Year − 2022) does look linear (although clearly it is’t, as it is bounded to [0,1], so a better fit would probably be something “arctan”y):
Also, it makes sense to me that uncertainty over “time until E” would behave more like a log-normal distribution (when the probability is fixed). That is, I’d expect that a forecaster’s estimate for years-until-AGI in particular probability p would itself be a lognormal distribution over the years (as I imagine the forecaster would be equally likely to be wrong by twice as many years or half as many years).
This justifies taking the geometric mean over the years (as it corresponds to an average over the log of the years), but not when looking at the probabilities.
Fitting the curve with a linear function (excluding the N/As), we get P(AGI at year y)=log(y−2022)/2−0.15
For y=2030, we’d get p=0.3
For y=2050, we’d get p=0.57
For y=2100, we’d get p=0.79
Or, for a probability p, we’d get the year y=102(p+0.15)+2022.
For p=0.1, we’d get y=2025
For p=0.5, we’d get y=2042
For p=0.9, we’d get y=2148
Overall, I got rather similar numbers 😊
Nice, thanks for the analysis.