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Let's go back to step II: Imagine that the coin that we're flipping isn't fair, and comes up heads with prior probability p. Further, suppose that the ratio be

Let's go back to step II: Imagine that the coin that we're flipping isn't fair, and comes up heads with prior probability p. Further, suppose that the ratio between the small population and the large population is R (in the article this is R = 10 / 100 = .1). In this situation, upon discovering that you're inside the small population, the posterior probability of heads ends up as p / (R - p * (1 - R)) So what if the coin is very unlikely to be heads instead of 50/50? If p = .001 (and we leave R = .1), our estimate of the probability heads after we observe that we are in the small population only comes up to about 1%. Thus, the real fallacy in the argument is that the choice of prior is unimportant. (If anyone tells you the prior is unimportant in any situation, they are wrong.) With a suitable estimate of the prior likelihood of Doom Soon, the posterior likelihood of Doom Soon is still low enough.

titanomachy 12y ago
I played around with the model a bit and based on a couple assumptions it can be scaled to P(Doom Soon) = x/(1+x) where x = B/b * d where B is the number of humans born in the Doom Late scenario, b is the number of humans born so far, and d is the prior probability of Doom Soon. Assumptions: a) the number of humans born between now and Doom Soon is negligible and b) the Doom Late scenario has many more humans than Doom Soon (B + b ~= B). Notice I made no assumptions about the prior, d. Of course d does matter, but the point is that as long as the number of humans in Doom Long is assumed to be large enough, the probability will go close to one even for very small d. For example, if we use a Doom Late population of 200 trillion like in the post, then we have 95% probability of Doom Soon even if d ~= 0.0001. That being said, I am still fairly unconvinced by this argument. It would have every intelligent species continually concluding that they are about to go extinct, right up until the moment that they either do go extinct or they achieve immortality and stop reproducing.
- typomatic 12y ago
  As B -> \infty, also t -> \infty. I'm reminded of the Fight Club quote: On a long enough timeline, the survival rate for everyone drops to zero. :)
  - titanomachy 12y ago
    Haha nice. Although, in this case we are looking ahead, basing our short-term survival on what a long-term survival would theoretically look like. So the more people there are in the hypothetical Doom Late, the more likely Doom Soon becomes. The more I think about this the more absurd it seems.
    - typomatic 12y ago
      Yeah, all this analysis (both what we've done and in the original article) are facile--a proper Bayesian treatment would have continuous priors/posteriors that would be a little more informative than an either-or. The problem you're seeing here is that if you make your possibilities "Humans live forever (even past the heat death of the universe)" or "All humans die in the next 10 minutes", you'll find that the chance that humans die in the next 10 minutes is really absurdly high.

titanomachy 12y ago

I played around with the model a bit and based on a couple assumptions it can be scaled to P(Doom Soon) = x/(1+x) where x = B/b * d where B is the number of humans born in the Doom Late scenario, b is the number of humans born so far, and d is the prior probability of Doom Soon. Assumptions: a) the number of humans born between now and Doom Soon is negligible and b) the Doom Late scenario has many more humans than Doom Soon (B + b ~= B). Notice I made no assumptions about the prior, d. Of course d does matter, but the point is that as long as the number of humans in Doom Long is assumed to be large enough, the probability will go close to one even for very small d. For example, if we use a Doom Late population of 200 trillion like in the post, then we have 95% probability of Doom Soon even if d ~= 0.0001. That being said, I am still fairly unconvinced by this argument. It would have every intelligent species continually concluding that they are about to go extinct, right up until the moment that they either do go extinct or they achieve immortality and stop reproducing.

typomatic 12y ago
As B -> \infty, also t -> \infty. I'm reminded of the Fight Club quote: On a long enough timeline, the survival rate for everyone drops to zero. :)
- titanomachy 12y ago
  Haha nice. Although, in this case we are looking ahead, basing our short-term survival on what a long-term survival would theoretically look like. So the more people there are in the hypothetical Doom Late, the more likely Doom Soon becomes. The more I think about this the more absurd it seems.
  - typomatic 12y ago
    Yeah, all this analysis (both what we've done and in the original article) are facile--a proper Bayesian treatment would have continuous priors/posteriors that would be a little more informative than an either-or. The problem you're seeing here is that if you make your possibilities "Humans live forever (even past the heat death of the universe)" or "All humans die in the next 10 minutes", you'll find that the chance that humans die in the next 10 minutes is really absurdly high.