Nice framework for structuring forecasts. The conjuction deflation problem in conditional chains is something I see constantly - people will say each step is "70% likely" without realizing that five steps at 70% each gives you 17% total. Had a project manager once who kept piling"probably fine" assumtions onto a roadmap and then was shocked when nothing shipped on time.
This is a nice technique, but I find this math is somehow missing some scale-awareness. Suppose we had taken our "period" for assessing the per-period probability to be months instead of years. Then we would have calculated a 1/(30*12 + 2) = 0.002762430939 per-month chance of satellite attack, and substituting in values appropriately to the above equation, we would get a slightly higher chance
1 - (1 - 1/(30*12 + 2))^12 ≈ 3.26%
If we had taken it to be a decade, then we would have calculated a 1/(3 + 2) = 0.2 per-decade chance of satellite attack, and substituting in values, we would get something lower:
1 - (1 - 1/(3 + 2))^(1/10) ≈ 2.21%
Is there some art to choosing the period over which we average? Is it a good idea to take the limit as the period gets smaller and smaller?
You're right that the choice of time unit affects the result. In practice, I think top forecasters try to pick the period that matches the natural rhythm of when the event could occur (e.g. maybe attacks are driven by campaigns that follow annual cycles). Ideally, a forecaster wouldn't rely on this analysis alone, but would balance it across different methods. When I'm done with this series, I'll probably want to write something about all the important considerations I had to leave out because they were too complicated to encode at this point.
Nice framework for structuring forecasts. The conjuction deflation problem in conditional chains is something I see constantly - people will say each step is "70% likely" without realizing that five steps at 70% each gives you 17% total. Had a project manager once who kept piling"probably fine" assumtions onto a roadmap and then was shocked when nothing shipped on time.
> 1−(1−1/32)^1 ≈ 3.1%.
This is a nice technique, but I find this math is somehow missing some scale-awareness. Suppose we had taken our "period" for assessing the per-period probability to be months instead of years. Then we would have calculated a 1/(30*12 + 2) = 0.002762430939 per-month chance of satellite attack, and substituting in values appropriately to the above equation, we would get a slightly higher chance
1 - (1 - 1/(30*12 + 2))^12 ≈ 3.26%
If we had taken it to be a decade, then we would have calculated a 1/(3 + 2) = 0.2 per-decade chance of satellite attack, and substituting in values, we would get something lower:
1 - (1 - 1/(3 + 2))^(1/10) ≈ 2.21%
Is there some art to choosing the period over which we average? Is it a good idea to take the limit as the period gets smaller and smaller?
You're right that the choice of time unit affects the result. In practice, I think top forecasters try to pick the period that matches the natural rhythm of when the event could occur (e.g. maybe attacks are driven by campaigns that follow annual cycles). Ideally, a forecaster wouldn't rely on this analysis alone, but would balance it across different methods. When I'm done with this series, I'll probably want to write something about all the important considerations I had to leave out because they were too complicated to encode at this point.