Humbali: I feel surprised that I should have to explain this to somebody who supposedly knows probability theory. If you put higher probabilities on AGI arriving in the years before 2050, then, on average, you’re concentrating more probability into each year that AGI might possibly arrive, than OpenPhil does. Your probability distribution has lower entropy. We can literally just calculate out that part, if you don’t believe me. So to the extent that you’re wrong, it should shift your probability distributions in the direction of maximum entropy.
[Is Humbali right that generic uncertainty about maybe being wrong, without other extra premises, should increase the entropy of one’s probability distribution over AGI, thereby moving out its median further away in time?]
The uncertainty must already be “priced in” your probability distribution. So your distribution and hence your median shouldn’t shift at all, unless you actually observe new relevant evidence of course.
The answer I came up with, before reading, is that the proper maxent distribution obviously isn’t uniform over every planck interval from here until protons decay; it’s also obviously not a gaussian with a midpoint halfway to when protons decay. But the next obvious answer is a truncated normal distribution. And that is not a thought conducive to sleeping well.
Going to try answering this one:
The uncertainty must already be “priced in” your probability distribution. So your distribution and hence your median shouldn’t shift at all, unless you actually observe new relevant evidence of course.
The answer I came up with, before reading, is that the proper maxent distribution obviously isn’t uniform over every planck interval from here until protons decay; it’s also obviously not a gaussian with a midpoint halfway to when protons decay. But the next obvious answer is a truncated normal distribution. And that is not a thought conducive to sleeping well.
If it’s a normal distribution, what’s the standard deviation?