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.
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.