On further reflection, both Ancestor and each Descendant can consider the proposition P(X) = “X is a descendant & X is a lottery winner”. Given the setup, Ancestor can quantify over X, and assign probability 1/N to each instance. That’s how the statement {”I” will win the lottery with probability 1} is to be read, in conjunction with a particular analysis of personal identity that warrants it. This would be the same proposition each descendant considers, and also assigns probability 1/N to. On this way of looking at it, both Ancestor and each descendant are in the same epistemic state, with respect to the question of who will win the lottery.
Ok, so far so good. This same way of looking at things, and the prediction about probability of descendants, is a way of looking at the Sleeping Beauty problem I tried to explain some months ago, and from what I can see is an argument for why Beauty is able to assert on Sunday evening what the credence of her future selves should be upon awakening (which is different from her own credence on Sunday evening), and therefore has no reason to change it when she later awakens on various occasions. It didn’t seem to get much traction then, probably because it was also mixed in with arguments about expected frequencies.
On further reflection, both Ancestor and each Descendant can consider the proposition P(X) = “X is a descendant & X is a lottery winner”. Given the setup, Ancestor can quantify over X, and assign probability 1/N to each instance. That’s how the statement {”I” will win the lottery with probability 1} is to be read, in conjunction with a particular analysis of personal identity that warrants it. This would be the same proposition each descendant considers, and also assigns probability 1/N to. On this way of looking at it, both Ancestor and each descendant are in the same epistemic state, with respect to the question of who will win the lottery.
Ok, so far so good. This same way of looking at things, and the prediction about probability of descendants, is a way of looking at the Sleeping Beauty problem I tried to explain some months ago, and from what I can see is an argument for why Beauty is able to assert on Sunday evening what the credence of her future selves should be upon awakening (which is different from her own credence on Sunday evening), and therefore has no reason to change it when she later awakens on various occasions. It didn’t seem to get much traction then, probably because it was also mixed in with arguments about expected frequencies.