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PlaidX comments on The Presumptuous Philosopher's Presumptuous Friend - Less Wrong
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Ah, so the difference isn't that I used hotels instead of universes, it's that I used hotels instead of POSSIBLE hotels. In other words, your likelihood of being in a hotel depends on the number of "you"s in the hotel, but your likelihood of being in a possible hotel does not, is that what you're saying?
Unless the number of "you"s is zero. Then it clearly does depend on the number. Isn't this just packing and unpacking?
You're reading a little more into what I said than was actually there. I was just remarking on the change of dependence between the parts of the problem, without having thought through what the consequences would be.
Now that I have thought it through, I agree with the presumptuous philosopher in this case. However I don't agree with him about the size of the universe. The difference being that in the hotel case we want a subjective probability, whereas in the universe case we want an objective one. Subjectively, there's a very high probability of finding yourself in a big universe/hotel. But subjective probabilities are over subjective universes, and there are very very many subjective large universes for the one objective large universe, so a very high subjective probability of finding yourself in a large universe doesn't imply a large objective probability of being found in one.
I don't understand what you mean by subjective and objective probabilities. Would you still agree with the philosopher in my problem if omega flipped a coin (or looked at binary digit 5000 of pi) and then built the small hotel OR the big hotel?
I don't know what I meant either. I remember it making perfect sense at the time, but that was after 35 hours without sleep, so.....
The answer to the second part is no, I would expect a 50:50 chance in that case.
In case you were thinking of this as a counterexample, I also expect a 50:50 chance in all the cases there from B onwards. The claim that the probabilities are unchanged by the coin toss is wrong, since the coin toss changes the number of participants, and we already accepted that the number of participants was a factor in the probability when we assigned the 99% probability in the first place.
So, if omega picks a number from 1 to 3, and depending on the result makes:
A. a hotel with a million rooms
B. a hotel with one room
C. a pile of flaming tires
you'd say that a person has a 50% chance of finding themselves in situation A or B, but a 0% chance of being in C?
Why does the number of people only matter when the number of people is zero? Doesn't that strike you as suspicious?
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?