Claire stole some of Bob's measure by resurrecting him. If she hadn't done the experiment, he'd have a 100% chance of finding himself in the 0.01% branch. Since she did resurrect him, he had a 99.99% chance of finding himself in the main branch and a 0.01% chance of finding himself in the smaller 0.01% branch.
I don't think this would invalidate the experiment - the chain of consciousness that died will only exist in one universe, and a different, related one will exist in all the others, since it redacts back to before the moment of death, not the exact moment.
I think it's pretty clear that the redaction machine could have redacted to the exact moment T of death, but that would have been more bother and would likely require major medical intervention to return Bob to health from that state. The fact that it went back further just means that some of Bob's experience was unwound to time T-X.
If you take a drug that prevents long-term memory formation for 5 minutes, does it kill the "you" that existed in that time? What about a device that reverts your brain and body state back 5 minutes? What if a year later you have just naturally forgotten everything about some 5 minute period? Did the person that existed in that 5 minutes die? If so, when?
I do agree that resurrection doesn't invalidate the experiment, but for a completely different reason: it was invalid even without the resurrection.
That is an interesting point. Perhaps I muddied the waters by making the reset take Bob to a time before the experiment was carried out. I did not consider the time of reset to be significant, perhaps foolishly. In your chain of consciousness model are their two branching evens? One at some time before the experiment is carried out where in a bunch of branches Bob finds himself suddenly pulled forwards in time, then a later event at the time of the quantum measurement? We could go down a rabbit hole on this with arguments from Bob like "well, I haven't found myself suddenly pulled into the future, so I must be in the branch where I survive".
My position (like JBlack) is that the experiment was invalid even without the resurrection. The primary aim of the story is to try and be funny, but the secondary aim is to try and sidestep all the arguments about whether the quantum suicide thought experiment actually makes logical sense (which can be quite subtle) by trying to work out if it proves too much. If the argument proves obvious nonsense then we know the logic is somehow flawed, even before we agree on exactly how. At least in my opinion the existence of resurrection technology (so that every Bob has further experiences, even the ones that die) raises serious problems for the thought experiment - as it seems to restore a symmetry between all the branches, so that singling out the one where Bob survives as more significant seems suspect. The (current) non-existence of resurrection technology doesn't seem relevant to me, as the many-worlds interpretation surely does not rule out the possibility of resurrection technology (or life after death). It would seem bizarre to me if our level of certainty on (1) life after death, or technological resurrection should be related to our certainty of (2) the many-worlds interpretation. And thus (2) should be independent of (1). Thus assuming a particular value for (1) (that resurrection is possible) should not move our opinions on (2).
Some silliness based on recent discussion of quantum suicide and the redaction machine.
Bob found himself, quite suddenly, in a chamber walled with hexagonal plates of gleaming copper.
Claire welcomed him back to life, and gave him some clothes.
"So, where am I?" asked Bob. He thought he remembered Claire from the lab. She worked in the group across the hall.
"You have just been reset back to life by a redaction machine. You died you see, so we used this experimental machine to bring you back. It unwinds an object to a previous state in time. We reset you back to how you were this morning."
"Yeah, I was on my way into the university. So, huh, how did I die?"
Claire frowned. "It was quite weird. You were having an argument with Alice about the many worlds interpretation of quantum mechanics. In order to prove to her that this theory was correct you built an apparatus that would use a quantum random number generator to kill you with 99.99% probability. And well, it killed you."
"What!" screamed Bob. "But, you don't understand. By bringing me back you have retroactively ruined the whole experiment..."
"Really?" Claire raised an eyebrow. "Can you explain how?"
"Well of course." said Bob. "See, if the many worlds interpretation of quantum mechanics is correct then, according to the anthropic principle, the only version of me left to update their priors after the apparatus activates is the one who survives. So I can only update towards believing in the many worlds interpretation. Therefore I can believe it with certainty, because I know that an arbitrary number of such experiments could be performed, and they would result in me believing the theory. If you know that a course of action would result in yourself believing something then you might as well jump ahead and believe it."
"But, if the counter-factual is enough, why did you actually kill yourself?"
"Well, the last thing I remember I was on the bus in to work. But I imagine the reason I did so was because I wanted to prove it to Alice. She never takes my theories seriously."
"She seemed quite distraught" said Claire. "It was lucky this prototype redaction machine was ready this very day. In a way you killing yourself was a bit of a boon to us, we really wanted to try a resurrection. Remember I was talking about it the group seminar last week."
Bob didn't remember, he had been checking his emails in that talk. "You shouldn't have done it without my approval." said Bob sternly. "You retroactively invalidated the experiment."
"You know, I think it sounds like you would rather be dead than admit to being wrong. Even before we resurrected you, you had failed, at least in this world line, to prove your point. The only reason you didn't have to admit to being wrong was that you were dead. That doesn't make you right - it just makes you dead and wrong."
"Whatever." said Bob, far from convinced. "Anyway, I was thinking. If this machine can re-set things to a previous state in time then I have a cool experiment to try. We prepare a quantum state, measure it in one basis, say position. Then reset it back and try a different basis. Then reset again and go back to the first basis. I think your redaction machine gives us a way to break the uncertainty principle. Or wait! Even better, we get a pair of entangled particles and redact one of them and …"
"Sorry, no. The narrator only allowed us to have redaction machines on the condition we didn't ask certain really nerdy questions. Those were on the list."
"Bummer."
"Yeah, I know right."