A note on the Doomsday Argument

Abstract

Suppose the gods create either one person or two persons (in succession). You find yourself newly created, and with no reason to prefer the one-person hypothesis H1 to the two-person hypothesis H2, so you assign them each a credence of 1/2. The gods now tell you that you are the first person created; call this evidence E1. You reason as follows: if H1 is true, then I was bound to be the first person created, whereas if H2 is true it was equally likely that I would be the second person created. That is, P(E1|H1) = 1 and P(E1|H2) = 1/2. Then by a simple application of Bayes’s theorem, P(H1|E1) = 2/3 and P(H2|E1) = 1/3. That is, the evidence that I am the first person created confirms H1 over H2