Duplication versus probability

I confess I don't really understand what problem this is attempting to show us, that explains why we shouldn't think of duplication and probability as alike and why Stuart has become less keen on "many worlds" approaches to QM. I mean, it describes some questions one can ask, and (so far as I can see) then just gestures towards them and invites us to feel bad about those questions. It seems like I'm missing a step in the argument.

Certain duplication is not the exact same thing as probability. But who ever said it was?

It is, however, somewhat like probability, and I don't see anything in this post that should change anyone's opinion about that.

It seems as if what Stuart says about "the thread of conscious experience" is intended to be an argument against the Everett interpretation, but I don't understand why. There's nothing consciousness-specific about quantum measure (or about probability); there is some sense in which, if mutually exclusive and exhaustive events A and B happen with measures 0.1 and 0.9 respectively, "9x as much of you" ends up in the B-worlds as in the A-worlds, but what does this mystical thread-of-experience language gain for us? It seems to me that these differences in measure are relevant precisely because they correspond to differences in probability, and e.g. I care 10x more about what happens to me in futures that are 10x as likely. Is there supposed to be something illegitimate about that?

Being a hopeless munchkin, I will note that the thought experiment has an obvious loophole: for the choice to truly be a choice, we would have to assume, somewhat arbitrarily, that using the duplication lever will disintegrate the machinery. Else, you could pull the lever to create a duplicate who'll deliver the message, and *then* the you at the bottom of the well could rip up the machinery and take their shot at climbing up.

I agree that duplication is not standard probability. Standard probability has no notion of an indexical so these situations end up overlapping.

There are two routes here as per A tree falls on sleeping beauty [LW · GW]. One is to go the halver route and handle duplications in the decision theory. The other is to go the thirder route and construct what I'll call an agent-state relative probability. Roughly, I mean a notion of probability that is concerned more with what fraction of agent-states will be correct than with any objective notion of probability. As I explained on my comment [LW(p) · GW(p)] to the paradoxes post, we shouldn't be surprised that a notion of probability specifically designed to be relative in this sense will be relative to what agents exist. So I'm more than happy to bite the bullet on the reductio ad absurdum.

If we can rule out thoughtcrime, we could have a large quantum computer simulate many environments with different goal systems in charge, then act as if the mechanics of indexical uncertainty don't work out to this already winning us the game.

If an exact copy of you were to be created, it would have to be stuck in the hole as well. If the 'copy' is not in the hole, then it is not you, because it is experiencing different inputs and has a different brain state.

But that's a question without meaning.

I don't think it is. There seems to be an effort not to use the term consciousness, but we need to talk consciousness to understand the difference. Either quantum copies share the same consciousness or they don't. Probabilities may or may not depend on this question – assuming the conclusions of your previous posts on the anthropic principle, I think they do. We can't answer that question, but we can understand that there is a question and grasp the conceptual difference. Discussing these issues without doing so seems fairly misguided to me.

After reading this I feel that how one should deal with anthropics strictly depends on goals. I'm not sure exactly which cognitive algorithm does the correct thing in general, but it seems that sometimes it reduces to "standard" probabilities and sometimes not. May I ask what does UDT say about all of this exactly?

Suppose you're rushing an urgent message back to the general of your army, and you fall into a deep hole. Down here, conveniently, there's a lever that can create a duplicate of you outside the hole. You can also break open the lever and use the wiring as ropes to climb to the top. You estimate that the second course of action has a 50% chance of success. What do you do?

Obviously, if the message is your top priority, you pull the lever, and your duplicate will deliver that message. This succeeds all the time, while the wire-rope only has 50% chance of working.

Agree.

after pulling the lever, do you expect to be the copy on the top or the copy on the bottom?

Question without meaning per se, agree.

what if the lever initially creates one copy - and then, five seconds later, creates a million? How do you update your probabilities during these ten seconds?

Before pulling the lever, I commit to do the following.

For the first five seconds, I will think (all copies of me will think) "I am above". This way, 50% of all my copies will be wrong.

For the remaining five seconds, I will think (all copies of me will think) "I am above". This way, one millionth of all my copies will be wrong.

If each of my copies was receiving money for distinguishing which copy he is, then only one millionth of all my copies would be poor.

This sounds suspiciously like updating probabilities the "standard" way, especially if you substitute "copies" with "measure".