I like this example because it has nice tidy prior probabilities. That’s very much lacking in the Doomsday Argument—how do you distribute a prior over a value that has no obvious upper bound? For any finite number of people that will ever live, is there much greater than zero prior probability of that being the number? Even if I can identify something truly special about the reference class “among the first 100 billion people” as opposed to any other mathematically definable group—and thus push down the posterior probabilities of very large numbers of people eventually living—it doesn’t seem to push down very far.
I like this example because it has nice tidy prior probabilities. That’s very much lacking in the Doomsday Argument—how do you distribute a prior over a value that has no obvious upper bound? For any finite number of people that will ever live, is there much greater than zero prior probability of that being the number? Even if I can identify something truly special about the reference class “among the first 100 billion people” as opposed to any other mathematically definable group—and thus push down the posterior probabilities of very large numbers of people eventually living—it doesn’t seem to push down very far.