The formula is just the fraction of people who live in a world where a given event happened. You take, (the number average number of persons in a world where an event took place * the probability of the event taking place), and divide it by, (the number average number of persons in a world where an event took place times the probability of the event taking place + the average number of persons in a world where the event didn’t take place * the probability of the event not taking place) Math is admittedly not my strong suit.
the two island example is just to give the simplest possible example, this is why there are only two. You are correct that there could be more people in post-catastrophe worlds.
Yeah, certainly we might rather know the percentage of worlds where the catastrophe occurred. The formula is useful because it lets you convert between the percentage of worlds in which a thing happens and the percentage of persons that thing happens to(if you know the average populations of worlds where the thing both happens and doesn’t)
I imagine the set of worlds to be identical up until the precise moment of the trinity test(July 16th, 1945 5:29 AM), however, this is just a narrative choice, and ultimately it’s kind of arbitrary. My suspicion is that the doomsday argument is valid due to space colonization being logistically impossible(or at least so implausible that it basically never happens/when space colonization does happen very few people actually live off-world due to logistical complications), and this is why we don’t find ourselves in a roman world. We might also just be in an unlikely circumstance.
The formula is just the fraction of people who live in a world where a given event happened. You take, (the number average number of persons in a world where an event took place * the probability of the event taking place), and divide it by, (the number average number of persons in a world where an event took place times the probability of the event taking place + the average number of persons in a world where the event didn’t take place * the probability of the event not taking place) Math is admittedly not my strong suit.
the two island example is just to give the simplest possible example, this is why there are only two. You are correct that there could be more people in post-catastrophe worlds.
Yeah, certainly we might rather know the percentage of worlds where the catastrophe occurred. The formula is useful because it lets you convert between the percentage of worlds in which a thing happens and the percentage of persons that thing happens to(if you know the average populations of worlds where the thing both happens and doesn’t)
I imagine the set of worlds to be identical up until the precise moment of the trinity test(July 16th, 1945 5:29 AM), however, this is just a narrative choice, and ultimately it’s kind of arbitrary. My suspicion is that the doomsday argument is valid due to space colonization being logistically impossible(or at least so implausible that it basically never happens/when space colonization does happen very few people actually live off-world due to logistical complications), and this is why we don’t find ourselves in a roman world. We might also just be in an unlikely circumstance.