Possible solution to the Fermi paradox: there is no paradox. The normal approaches find that there should be a very large number of civilizations by plugging point estimates into the Drake Equation, but multiplying point estimates (as opposed to probability distributions) with each other gives you misleading results.
As a toy example, if you multiply nine factors together to get a probability of life per star, each of the factors a random real number drawn uniformly from [0, 0.2] and the point estimate for each being 0.1, then the product of the point estimates is 1 in a billion. This would translate to an expected 100 life-bearing stars, given 100 billion stars. But if you instead combine the probability distributions, you get a median number of 8.7 life-bearing stars (the mean is still 100).
Going through the literature to estimate reasonable prior distributions for different values in the Drake Equation, you get much more pessimistic estimates for the probability of life in the universe; the priors chosen by the authors suggest a 40% a priori chance for life only emerging once. We really might just be alone.
EY wrote that multiplying point estimates are not correct for estimating the probability of success of cryonics. https://www.jefftk.com/p/multiple-stage-fallacy However, it looks like his conclusion is that the total probability of success should be higher than implied by multiplication, not lower as in case of Sanders’ presentation. This may be because in his case most probabilities are above 0.5, so in fact multiplication of the failure probabilities would give lower estimate. That is the probability of cryonic failure is smaller than predicted by multiplication of probabilities of failure on each step.
Nice idea, but I don’t think the cases aren’t mathematically analogous. Eliezer is just talking about multiplying probabilities, not estimates of anything. And he’s saying that that won’t produce the right answer because of human biases, not because it’s mathematically invalid. Whereas in the Drake equation we are multiplying probability distributions for certain parameters (the frequencies at which the various conditions for life occur) and it’s a mathematical fact that the median of the product isn’t the product of the medians.
My summary:
Possible solution to the Fermi paradox: there is no paradox. The normal approaches find that there should be a very large number of civilizations by plugging point estimates into the Drake Equation, but multiplying point estimates (as opposed to probability distributions) with each other gives you misleading results.
As a toy example, if you multiply nine factors together to get a probability of life per star, each of the factors a random real number drawn uniformly from [0, 0.2] and the point estimate for each being 0.1, then the product of the point estimates is 1 in a billion. This would translate to an expected 100 life-bearing stars, given 100 billion stars. But if you instead combine the probability distributions, you get a median number of 8.7 life-bearing stars (the mean is still 100).
Going through the literature to estimate reasonable prior distributions for different values in the Drake Equation, you get much more pessimistic estimates for the probability of life in the universe; the priors chosen by the authors suggest a 40% a priori chance for life only emerging once. We really might just be alone.
Could we generalise this approach?
EY wrote that multiplying point estimates are not correct for estimating the probability of success of cryonics. https://www.jefftk.com/p/multiple-stage-fallacy However, it looks like his conclusion is that the total probability of success should be higher than implied by multiplication, not lower as in case of Sanders’ presentation. This may be because in his case most probabilities are above 0.5, so in fact multiplication of the failure probabilities would give lower estimate. That is the probability of cryonic failure is smaller than predicted by multiplication of probabilities of failure on each step.
Nice idea, but I don’t think the cases aren’t mathematically analogous. Eliezer is just talking about multiplying probabilities, not estimates of anything. And he’s saying that that won’t produce the right answer because of human biases, not because it’s mathematically invalid. Whereas in the Drake equation we are multiplying probability distributions for certain parameters (the frequencies at which the various conditions for life occur) and it’s a mathematical fact that the median of the product isn’t the product of the medians.