I will here consider what happens if you ignore such indexical information, conditioning only on the fact that someone in the universe with your memories exists. I refer to this procedure as “Full Non-indexical Conditioning” (FNC).
Note however that Neal says this idea implies that the thirder answer is correct in Sleeping Beauty:
In this regard, note that the even though the experiences of Beauty upon wakening on Monday and
upon wakening on Tuesday (if she is woken then) are identical in all “relevant” respects, they
will not be subjectively indistinguishable. On Monday, a fly on the wall may crawl upwards; on
Tuesday, it may crawl downwards. Beauty’s physiological state (heart rate, blood glucose level,
etc.) will not be identical, and will affect her thoughts at least slightly. Treating these and other
differences as random, the probability of Beauty having at some time the exact memories and
experiences she has after being woken this time is twice as great if the coin lands Tails than
if the coin lands Heads, since with Tails there are two chances for these experiences to occur
rather than only one. This computation assumes that the chance on any given day of Beauty
experiencing exactly what she finds herself experiencing is extremely small, as will be the case
in any realistic version of the experiment.
Assuming your idea is the same as FNC, I think from a decision theory perspective it’s still worse than just not updating. See this comment of mine under a previous post about FNC.
It looks like I should actually claim priority for this idea myself, since I came up with something very similar on the way to UDT. From this 1998 post:
One piece of information about the real universe you have direct access to
is your own mind state. This is captured in the statement D = “The real
universe contains at least one person with mind state M” where M is your
current mind state. I’m going to assume this is the ONLY piece of
information about the real universe you have direct access to. Everything
else must be computed from the prior and this data. The justification for
this is that I can’t think of any other information that is not part of or
derived from D.
Right away you know that any universe that does not contain at least one
person with mind state M cannot be real. It’s also not hard to see that
for any two universes that both contain at least one person with mind
state M, the ratio of their posterior probabilities is the same as the
ratio of their priors. This means the universe most likely to be real
given D is the one that has the highest prior among the universes that
contain at least one person with mind state M.
Well, I wouldn’t be surprised if a bunch of people have come up with similar ideas, but in the post you link to, you apply it only to a rather strange scenario in which the universe is the output of a program, which is allowed to simply generate all possible bit strings, and then decide that in this context the idea has absurd consequences. So I’m not sure that counts as coming up with it as an idea to take seriously...
But I took it seriously enough to come up with a counter-argument against it. Doesn’t that count for something? :)
To be clear I’m referring to the second post in that thread, where I wrote:
Let me try to generalize the argument that under the universal prior the
1UH gives really wierd results. The idea is simply that any sufficiently
large and/or long universe that doesn’t repeat has a good chance of
including a person with mind state M, so knowing that at least one person
with mind state M exists in the real universe doesn’t allow you to
eliminate most of them from the set of possible universes. If we want to
get a result that says the real universe is likely to be in a class of
intuitively acceptable universes, we would have to build that directly
into our prior. That is, make them a priori more likely to be real than
all other large/long universes.
Several questions follow if this argument is sound. First, is it
acceptable to consciously construct priors with a built in preference for
intuitively acceptable universes? If so how should this be done? If not
the 1UH is not as intuitive as we thought. We would have to either reject
the 1UH or accept the conclusion that the real universe is likely to be
really weird.
(In that post 1UH refers to the hypothesis that only one universe exists, and I was apparently assuming that what you call FNC is the only way to do Bayesian updating under 1UH so I was thinking this is an argument against 1UH, but looking at it now, it’s really more of an argument against FNC.)
Rather than abandon FNC for the reason you describe, I make the meta-argument that we don’t know that the universe is actually large enough for FNC to have problems, and it seems strange that local issues (like Doomsday or Sleeping Beauty) should depend on this. So whatever modifications to FNC might be needed to make it work in a very large universe should in the end not actually change the answers FNC gives for such problems when a not-incredibly-large universe is assumed.
Do you see your “not updating” scheme as the appropriate new theory applicable to very large universes? If so, does it in fact give the same result as applying FNC while assuming the universe is not so large?
Do you see your “not updating” scheme as the appropriate new theory applicable to very large universes?
It doesn’t fully solve problems associated with very large universes, but I think it likely provides a framework in which those problems will eventually be solved. See this post for more details.
See also this post which explains my current views on the nature of probabilities, which may be needed to understand the “not updating” approach.
If so, does it in fact give the same result as applying FNC while assuming the universe is not so large?
Sort of. As I explained in a linked comment, when you apply FNC you assign zero probability to the universes not containing someone with your memories and then renormalize the rest, but if your decisions have no consequences in the universes not containing someone with your memories, you end up making the same decisions whether you do this “updating” computation or not. So “not updating” gives the same result in this sense.
I’d forgotten this argument (I think I made it myself a few times too). I’m planning a new post to see what can be done about it (for some reason, I can’t edit my current post to add a caveat).
This seems very similar to Radford Neal’s full non-indexical conditioning:
Note however that Neal says this idea implies that the thirder answer is correct in Sleeping Beauty:
Assuming your idea is the same as FNC, I think from a decision theory perspective it’s still worse than just not updating. See this comment of mine under a previous post about FNC.
It looks like I should actually claim priority for this idea myself, since I came up with something very similar on the way to UDT. From this 1998 post:
Well, I wouldn’t be surprised if a bunch of people have come up with similar ideas, but in the post you link to, you apply it only to a rather strange scenario in which the universe is the output of a program, which is allowed to simply generate all possible bit strings, and then decide that in this context the idea has absurd consequences. So I’m not sure that counts as coming up with it as an idea to take seriously...
But I took it seriously enough to come up with a counter-argument against it. Doesn’t that count for something? :)
To be clear I’m referring to the second post in that thread, where I wrote:
(In that post 1UH refers to the hypothesis that only one universe exists, and I was apparently assuming that what you call FNC is the only way to do Bayesian updating under 1UH so I was thinking this is an argument against 1UH, but looking at it now, it’s really more of an argument against FNC.)
Rather than abandon FNC for the reason you describe, I make the meta-argument that we don’t know that the universe is actually large enough for FNC to have problems, and it seems strange that local issues (like Doomsday or Sleeping Beauty) should depend on this. So whatever modifications to FNC might be needed to make it work in a very large universe should in the end not actually change the answers FNC gives for such problems when a not-incredibly-large universe is assumed.
Do you see your “not updating” scheme as the appropriate new theory applicable to very large universes? If so, does it in fact give the same result as applying FNC while assuming the universe is not so large?
It doesn’t fully solve problems associated with very large universes, but I think it likely provides a framework in which those problems will eventually be solved. See this post for more details.
See also this post which explains my current views on the nature of probabilities, which may be needed to understand the “not updating” approach.
Sort of. As I explained in a linked comment, when you apply FNC you assign zero probability to the universes not containing someone with your memories and then renormalize the rest, but if your decisions have no consequences in the universes not containing someone with your memories, you end up making the same decisions whether you do this “updating” computation or not. So “not updating” gives the same result in this sense.
Ok, I’ve revised the idea entirely.
See here for why FNC doesn’t work as a probability theory (and neither do SIA or SSA): https://www.lesswrong.com/posts/iNi8bSYexYGn9kiRh/paradoxes-in-all-anthropic-probabilities
See here for how you can use proper scoring functions to answer the probability of seeing alien life in the galaxy; depending on whether you average the scores or total them, you get SSA-style or SIA-style answers: https://www.lesswrong.com/posts/M9sb3dJNXCngixWvy/anthropics-and-fermi
I’d forgotten this argument (I think I made it myself a few times too). I’m planning a new post to see what can be done about it (for some reason, I can’t edit my current post to add a caveat).
Huh, what is preventing you from editing your post?
It seemed it was a general lesswrong problem, now fixed; update done.