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 $P\left(\text{AGI at year}y\right)=\log (y-2022)/2-0.15$

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 $y={10}^{2(p+0.15)}+2022$. 

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 😊

The adversarial Turing test seems like an odd definition to forecast on. Nuno's linked blogpost makes one side of the argument well: There could be ways to identify an AI as different from a human long after AI becomes economically transformative or capable of taking over the world. On the other side, AI that passes an adversarial Turing test could still fail to have economic impact (perhaps because of regulation, or maybe it's too expensive to replace human labor) or pose a meaningful existential risk (because it's not goal directed, misaligned, or capable of overpowering humanity). 

I'd be more interested in your forecasts on a few other operationalizations of AI timelines:

• Economic impact, as measured by GDP growth rate or AI as % of inputs to GDP, seems like an important aggregate to track and forecast. It has the important quality of being easily verifiable and continuous over time, making forecasts easy to validate with each passing year. On the other hand, economic impact will likely lag cutting edge capabilities, which might pose the most x-risk. 
• X-Risk is what I actually care about. With all the debate over whether AI x-risk is disjunctive or conjunctive, I wouldn't want to use a model split into "Will we get AGI, and if so, will x-risks be realized?" that has clear cases where x-risk could occur without first meeting the AGI definition. A tougher question is whether to forecast the exact date of human disempowerment, or a preceding "point of no return", or another set of ideas. But all of these seem more directly aimed at the most important question of x-risk. 
• A particularly clean decomposition is "In what year will world energy consumption first exceed 130% of every prior year?" from Matthew Barnett's Metaculus question. This is designed to forecast transformative AI while accounting for the possibility that AI will overpower humanity, causing GDP to collapse as AI seizes all available resources for its own goal. Forecasting both this question and the economic impact question might show your x-risk estimate in the difference, unless you think that AI could overpower humanity without  transformative industrial capacity. 

Your thinking on these questions has been pretty persuasive to me, especially Nuno's recent blog and Eli Lifland's writeup of thinking through the full case. It's nice to get a perspective that's just a bit outside of the constant AI hype bubble. But these forecasts just felt a bit less informative than they could otherwise be, driven by edge cases around the definition. Curious if you would disagree with the importance of those edge cases, or think other forecasting targets have important flaws. 

In case people are interested, while updating updating Epoch's Literature Review of AI Timelines with this new forecast, I created a small notebook which uses a slightly different approach to aggregating the individual forecasts. Briefly, I fit a Gamma distribution to each forecast, which produces a CDF. Then, I combine the fitted CDFs using the geometric mean of odds. (This general approach is inspired by what AI Impacts has done in their expert surveys, although they use a different method of aggregating the fitted CDFs.) The final results are pretty similar, although a little more aggressive in the short- and longer-term, and a little less aggressive in the medium-term:

P(AGI by ___):

• 2030: 28%
• 2050: 59%
• 2100:  89%

Year when P(AGI) reaches ___:

• 10%: 2024
• 50%: 2043
• 90%: 2104

The notebook also includes some simple plots of the forecasts which you can play with.

Are you making short term (e.g. 1 year) AI-related forecasts, too? It would be helpful to figure out how much weight to give to your forecasts in this domain (and between individual forecasters), and may also give useful feedback for your longer range forecasts.