I don’t know how much my calculations are different from yours as I hasn’t been able to comprehend how to use your formula. Can you give me an elaborate example of using it, step-by-step?
“We can’t know that it is more likely that we are in a world that hasn’t experienced nuclear war, we are however justified in believing that it is more likely that we would be in a world that hasn’t experienced nuclear war.” Sorry, but I fail to see the difference between “it is more likely that we are in a world that hasn’t experienced nuclear war” and “it is more likely that we would be in a world that hasn’t experienced nuclear war”
1.”Y=AX/((AX)+(B(1-X))” How have you got this formula? Sorry, my probability math is a bit rusty, so maybe I’m missing something obvious.
2.I find it a poor choice to use two islands as your example. In context of this problem we deals with two sets, and each set >1. Even more, such example biases us to think that an observer to be moke likely to belong to a set of worlds where catastrophe hasn’t happened, as there are only two islands. It doesn’t need to be the case. While each world that experienced catastrophe is less populated, combined population of post-catastrophe worlds can be still greater than population of no-catastrophe worlds if there is too many of post-catastrophe worlds and too few no-catastrophe worlds. IMHO, it would be better to use set A (islands where volcanic eruption happened) and set B (islands where were no volcanic eruptions).
3.”So the probability of being on an island that has had a volcanic eruption is 1⁄3 ” Why would we want to know this? I think that calculation of risk of catastrophe (i.e. share of ruined worlds/islands) is much more relevant.
4.It’s unclear to me how you select worlds among which M.A.D. either happened or didn’t. For an example, in my comment I limited myself to all worlds where I was born. If you don’t do the same, then you will run into problems. Consider this. There are parallel worlds where Roman civilization never crumbled. Where they had time to achieve everything that current Western civilization achieved + several addtional centuries to go beyond this. In 2022 there would be Roman worlds that colonized several planets of Solar system, maybe even terraformed them and found ways to sustainably support much bigger population than 8 billions. It seems plausible for population to be distributed heavely in favor of Roman worlds in current year 2022. Yet you and me aren’t is a Roman world. Curious, don’t you think?