Yes, I agree that the space of things to be uncertain about is multidimensional. We project the uncertainty onto a one-dimensional space parameterized by “probability of <event> by <time>”.
It would be surprising for a sophisticated person to show a market of 49 @ 51 on this event. (Unpacking jargon, showing this market means being willing to buy for 49 or sell at 51 a contract which is worth 100 if the hypothesis is true and 0 if it is false)
(it’s somewhat similar saying that your 2-sigma confidence interval around the “true probability” of the event is 49 to 51. The market language can be interpreted with just decision theory while the confidence interval idea also requires some notion of statistics)
My interpretation of the second-hand evidence about Shane Legg’s opinion suggests that Shane would quote a market like 40 @ 60. (The only thing I know about Shane is that they apparently summarized their belief as 50% a number of years ago and hasn’t publicly changed their opinion since)
Perhaps I’m misinterpreting you, but I feel like this was intended as disagreement? If so, I’d appreciate clarification. It seems basically correct to me, and consistent with what I said previously. I still think that: if, in 2011, you gave 10% probability by 2018 and 50% by 2028; and if, in 2019, you still give 50% by 2028 (as an explicit estimate, i.e. you haven’t just not-given an updated estimate); then this is surprising, even acknowledging that 50% is probably not very precise in either case.
Yes, I agree that the space of things to be uncertain about is multidimensional. We project the uncertainty onto a one-dimensional space parameterized by “probability of <event> by <time>”.
It would be surprising for a sophisticated person to show a market of 49 @ 51 on this event. (Unpacking jargon, showing this market means being willing to buy for 49 or sell at 51 a contract which is worth 100 if the hypothesis is true and 0 if it is false)
(it’s somewhat similar saying that your 2-sigma confidence interval around the “true probability” of the event is 49 to 51. The market language can be interpreted with just decision theory while the confidence interval idea also requires some notion of statistics)
My interpretation of the second-hand evidence about Shane Legg’s opinion suggests that Shane would quote a market like 40 @ 60. (The only thing I know about Shane is that they apparently summarized their belief as 50% a number of years ago and hasn’t publicly changed their opinion since)
Perhaps I’m misinterpreting you, but I feel like this was intended as disagreement? If so, I’d appreciate clarification. It seems basically correct to me, and consistent with what I said previously. I still think that: if, in 2011, you gave 10% probability by 2018 and 50% by 2028; and if, in 2019, you still give 50% by 2028 (as an explicit estimate, i.e. you haven’t just not-given an updated estimate); then this is surprising, even acknowledging that 50% is probably not very precise in either case.