When we speak of a subjective probability in a person-multiplying experiment such as this, we (or at least, I) mean “The outcome ratio experienced by a
person who was randomly chosen from the resulting population of the experiment, then was used as the seed for an identical experiment, then was
randomly chosen from the resulting population, then was used as the seed.… and so forth, ad infinitum”.
I’m not confident that we can speak of having probabilities in problems which can’t in theory be cast in this form.
In other words, the probability is along a path. When you look at the problem this way, it throws some light on why there are two different arguable
values for the probability. If you look back along the path, (“what ratio will our person have experienced”) the answer in your experiment is 1000000:1.
If you look forward along the path, (“what ratio will our person experience”) the answer is 1:1 (in the flaming-tires case there’s no path,
so there’s no probability).
But again I must ask, on the going-forward basis, why is the number of people in each world irrelevant? I grant you that the WORLD splits into even thirds, but the people in it don’t, they split 1000000 / 1 / 0. Where are you getting 1 / 1 / 0?
Because if you agree that the correct way to measure the probability is as the occurrence ratio along the path, the degree of splitting is only significant to the extent that it affects the occurrence ratio, which in this case it doesn’t. The coin toss chooses
equiprobably which hotel comes next, then it’s on to the next coin toss to equiprobably choose which hotel comes next, and so forth. So each path has on average equal numbers of each hotel, going forwards.
But you’re not a hotel, you’re an observer. Why does the number of hotels matter but not the number of observers? If the tire fire is replaced with an empty hotel, you still can’t end up in it.
It seems like your function for ending up in a future, based on the number of observers in that future, goes as follows:
If there’s zero, the prior likelihood gets multiplied by zero.
If there’s one, the prior likelihood gets multiplied by one.
If there’s more than one, the prior likelihood still only gets multiplied by one.
This function seems more complicated than just multiplying the prior probability by the number of observers, which is what I do. My reasoning is, even on a going forward basis, if there’s a line connecting me to a world with one future self, and no line connecting me to a world without a future self, there must be 14 lines connecting me to a future with 14 future selves.
Is there some reason to prefer your going-forward interpretation over mine, despite the fact that mine is simpler and agrees with the going-backwards perspective?
When we speak of a subjective probability in a person-multiplying experiment such as this, we (or at least, I) mean “The outcome ratio experienced by a person who was randomly chosen from the resulting population of the experiment, then was used as the seed for an identical experiment, then was randomly chosen from the resulting population, then was used as the seed.… and so forth, ad infinitum”.
I’m not confident that we can speak of having probabilities in problems which can’t in theory be cast in this form.
In other words, the probability is along a path. When you look at the problem this way, it throws some light on why there are two different arguable values for the probability. If you look back along the path, (“what ratio will our person have experienced”) the answer in your experiment is 1000000:1. If you look forward along the path, (“what ratio will our person experience”) the answer is 1:1 (in the flaming-tires case there’s no path, so there’s no probability).
But again I must ask, on the going-forward basis, why is the number of people in each world irrelevant? I grant you that the WORLD splits into even thirds, but the people in it don’t, they split 1000000 / 1 / 0. Where are you getting 1 / 1 / 0?
Because if you agree that the correct way to measure the probability is as the occurrence ratio along the path, the degree of splitting is only significant to the extent that it affects the occurrence ratio, which in this case it doesn’t. The coin toss chooses equiprobably which hotel comes next, then it’s on to the next coin toss to equiprobably choose which hotel comes next, and so forth. So each path has on average equal numbers of each hotel, going forwards.
But you’re not a hotel, you’re an observer. Why does the number of hotels matter but not the number of observers? If the tire fire is replaced with an empty hotel, you still can’t end up in it.
It seems like your function for ending up in a future, based on the number of observers in that future, goes as follows:
If there’s zero, the prior likelihood gets multiplied by zero.
If there’s one, the prior likelihood gets multiplied by one.
If there’s more than one, the prior likelihood still only gets multiplied by one.
This function seems more complicated than just multiplying the prior probability by the number of observers, which is what I do. My reasoning is, even on a going forward basis, if there’s a line connecting me to a world with one future self, and no line connecting me to a world without a future self, there must be 14 lines connecting me to a future with 14 future selves.
Is there some reason to prefer your going-forward interpretation over mine, despite the fact that mine is simpler and agrees with the going-backwards perspective?