The first elementary error is that the Doomsday Argument conflates total duration and future duration.
I don’t fully understand the problem. In mine, I did everything with total duration, and used the fact that we know we’ve been here this long to update on the total not being less than the current.
Then I noticed that there being other planets actually makes a difference, and I can find the average of the totals for different planets, but it can fall below our current value. The actual value depends on a probability distribution I’m not sure how to find, but I think the difference will be around lasting one or two orders of magnitude longer.
The second elementary error is the Doomsday Argument’s use of the Self-Sampling Assumption, which is contradicted by the prior information in all attempts at real-life applications in the literature.
I’m not sure what’s going on here. My assumption is that we don’t fully understand what the dangers are, and thus have to rely on our priors. To the extent that we haven’t processed the evidence, its expected value will match our priors in accordance with conservation of expected evidence.
I’ve made a post about a Bayesian doomsday argument.
I don’t fully understand the problem. In mine, I did everything with total duration, and used the fact that we know we’ve been here this long to update on the total not being less than the current.
Then I noticed that there being other planets actually makes a difference, and I can find the average of the totals for different planets, but it can fall below our current value. The actual value depends on a probability distribution I’m not sure how to find, but I think the difference will be around lasting one or two orders of magnitude longer.
I’m not sure what’s going on here. My assumption is that we don’t fully understand what the dangers are, and thus have to rely on our priors. To the extent that we haven’t processed the evidence, its expected value will match our priors in accordance with conservation of expected evidence.
Your use of the Jeffreys prior—P(T=n) ∝ 1/n—is the exception I mention: Gott (1994, 108) uses the Jeffreys prior.