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.
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.