Concerning the second claim, there is no ground from which to assume such symmetry. The first event could be, for all we know, 10^-32, and the second event 10^-10; or vice versa. So a lack of knowledge about those probabilities doesn’t imply that the two comparable.
But if we don’t know which one’s which, aren’t our subjective probabilities of each destroying the world equal anyway?
It can be argued against this conclusion that one usually assumes that we are allowed to ignore extremely unlikely hypotheses in our decisions. Consider, say, the hypothesis that having a cup of tea would result in the destruction of the universe. Surely, the argument goes, we don’t need to consider all logically possible hypotheses? My response to this criticism is that we don’t consider all possible hypotheses because we make a pre-judgement that no further hypotheses would change our decisions and that further considerations would only introduce unnecessary complications in the calculations. Most tea drinkers attribute an exceedingly small probability for the destruction of the universe conditional on their drinking tea. But if a tea drinker were to give any appreciable probability to this hypothesis, it would certainly be irrational for them to have that cup of tea.
Further, in a situation like the referee’s example, not only would these kinds of unlikely hypotheses have negligible effects on the decisions but there would also usually be equally arbitrary competing hypotheses pulling the decision the other way: The hypothesis that NOT having a given cup of tea will lead to the destruction of the universe is just as (un)likely as the one that having that cup of tea will do so and precisely cancels the effect of the first.
It does not sound as if the author is assuming an uninformative prior with respect to the universe-destroying capabilities of tea, but that would explain the symmetry argument.
But if we don’t know which one’s which, aren’t our subjective probabilities of each destroying the world equal anyway?
I may have misread the original section:
It does not sound as if the author is assuming an uninformative prior with respect to the universe-destroying capabilities of tea, but that would explain the symmetry argument.