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Stuart_Armstrong comments on Papers framing anthropic questions as decision problems? - Less Wrong
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To translate this into ADT terms: in problem 2, the coin is fair, in problem 1, the coin is (1/3, 2/3) on (H, T) (or maybe the coin was fair, but we got extra info that pushed the postiori odds to (1/3, 2/3)).
Then ADT (and SSA) says that selfish agents should bet up to 2/3 of candybar on Tails in problem 1, and 1/2 in problem 2. Exactly the same as what you were saying. I don't understand why you think that ADT would make identical choices in both problems.
The reason that's "exactly as I was saying" is because you adjusted a free parameter to fit the problem, after you learned the subjective probabilities. The free parameter was which world to regard as "normal" and which one to apply a correction to. If you already know that the (1/2, 1/4, 1/4) problem is the "normal" one, then you already solved the probability problem and should just maximize expected utility.
Er no - you gave me an underspecified problem. You told me the agents were selfish (good), but then just gave me anthropic probabilities, without giving me the non-anthropic probabilities. I assumed you were meaning to use SSA, and worked back from there. This may have been incorrect - were you assuming SIA? In that case the coin odds are (1/2,1/2) and (2/3,1/3), and ADT would reach different conclusions. But only because the problem was underspecified (giving anthropic probabilities without explaining the theory that goes with them is not specifying the problem).
As long as you give a full specification of the problem, ADT doesn't have an issue. You don't need to adjust free parameters or anything.
I feel like I'm missing something here. Can you explain the hole in ADT you seem to find so glaring?
I intended "In both of these problems there are two worlds, "H" and "T," which have equal "no anthropics" probabilities of 0.5. "
In retrospect, my example of evidence (stopping some of the experiments) wasn't actually what I wanted, since an outside observer would notice it. In order to mess with anthropic probabilities in isolation you'd need to change the structure of coinflips and people-creation.
But you can't mess with the probabilities in isolation. Suppose I were an SIA agent, for instance; then you can't change my anthropic probabilities without changing non-anthropic facts about the world.
I'm uncertain whether what you're saying is relevant. The question at hand is, is there some change to a problem that changes anthropic probabilities, but is guaranteed not to change ADT decisions? Such a change would have to conserve the number of worlds, the number of people in each world, the possible utilities, and the "no anthropics" probabilities
For example, if my anthropic knowledge says that I'm an agent at a specific point in time, a change in how long Sleeping Beauty stays awake in different "worlds" will change how likely I am to find myself there overall.
Is there? It would require some sort of evidence that would change your own anthropic probabilities, but that would not change the opinion of any outside observer if they saw it.
Doesn't feel like that would work... if you remember how long you've been awake, that makes you into slightly different agents, and if the duration of the awakening gives you any extra info, it would show up in ADT too. And if you forget how long you're awake, that's just sleeping beauty with more awakenings...
Define "individual impact" as the belief that your own actions have no correlations with those of your copies (the belief your decisions control all your copies is "total impact"). Then ADT basically has the following equivalences:
If those equivalences are true, it seems that we cannot vary the anthropic probabilities without varying the ADT decision.
EDIT: Expanded first point a bit.
Hm. One could try and fix it by splitting each point in time into different "worlds," like you suggest below. But the updating from time (let's assume there's no clock to look at, so the curves are smooth) would rely on the subjective probabilities, which you are avoiding. The update ratio is P(feels like 4 hours | heads) / P(feels like 4 hours). If P(feels like 4 hours | X) is 0.9 if X is heads and 0.8 if X is tails, then if the probabilities are 1/3 the ratio will be 1.08, while if the probabilities are 1/2, 1/4, 1/4 the update is a factor of 1.059.
This does lead to a case a bit more complicated than my original examples, though, because the people in different worlds will make different decisions. I'm not even sure how ADT would handle this situation, since it has to avoid the subjective probabilities - do you respond like an outside observer, and use 0.5, 0.5 for everything?
Yes, that would be reasonable.
Those only hold if things are simple. To say "these might prevent things from getting any more complicated" is to put the cart before the horse.
ADT does not avoid subjective probabilities - it only avoid anthropic probabilities. P(feels like 4 hours | heads) is perfectly fine. ADT only avoids probabilities that would change if you shifted from SIA to SSA or vice versa.
It is exactly one of those probabilities.