How to deal with probabilities in the presence of clones?
post by depressurize (anchpop) · 2021-09-15T17:01:28.768Z · LW · GW · 3 commentsThis is a question post.
Contents
Answers 4 JBlack 0 Measure -1 Pablo Repetto None 3 comments
You find yourself in a room. You know there are only two possible ways you could have gotten into the room, and just a moment earlier you considered them both equally likely:
A: I make 8 identical copies of you and put them in totally identical rooms. A minute passes, then I instantly kill 7 of the copies. (Also, I don't think it matters but your cognition is deterministic, so you know all 8 copies of you stay perfectly in sync until I kill 7 of them.)
B: I make one copy of you and put it in a room. A minute passes, then I do something that has a 7/8 chance of instantly killing the copy.
Now you've appeared in the room, but a minute hasn't passed yet. Regardless of whether A or B is true, you'd experience the same thing either way. Does your estimation of the odds of A:B change?
Now a minute passes and you're still alive. Des your estimation of the odds of A:B change now?.
Answers
The number of observers in the possible worlds given their observations are 8 for A and 1 for B (with weighting 1/2 each) before 1 minute passes. So SIA says that the odds are 8:1 in favour of A at that time. The weighted number of observers who survive more than a minute is 1/2 for A and 1/16 for B, so the odds remain unchanged at 8:1 in favour of A.
Under SSA there are equal odds of scenarios A and B, which don't change in the first minute since they are observationally indistinguishable. After a minute, scenario B(i) in which the clone lives and scenario A are still indistinguishable, with weightings 1/2 and 1/16 respectively. B(ii) is ruled out, so the updated odds are 8:1 in favour of A.
This analysis is unchanged if you replace "is killed" by "is told which scenario they're in" and condition on a minute passing and not being told which scenario you were in.
Immediately upon finding myself in the room, I could be the single copy in scenario B or any of the 8 copies in scenario A. I think I would have to assign 8:1 odds for A:B. Either way, I have a 7/8 chance of dying after a minute. After 1 minute, there is 1 clone in scenario A and 1/8 of a clone in scenario B, so I'm still at 8:1 odds for A:B.
No and no.
When I appear in the room I observe that I exist, but I couldn't have observed that I didn't exist, thus I don't update.
When a minute passes I observe that I survived, but I couldn't have observed that I didn't survive, thus I don't update.
3 comments
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comment by Dagon · 2021-09-15T17:44:06.826Z · LW(p) · GW(p)
Seems a trivial reworking of https://www.lesswrong.com/tag/sleeping-beauty-paradox [? · GW] . The answer depends on what you're predicting - how will your future experience differ between A and B?
comment by Vladimir_Nesov · 2021-09-15T20:13:18.785Z · LW(p) · GW(p)
Meta: At the time of writing this comment, before I strong-upvote the question, it sits at -3, with two non-author votes. This is not very welcoming (this is the author's first post/comment here). The only thing wrong with the question seems to be that the author isn't already aware of the standard way of pointing at the same cluster of issues (which is exactly the situation where asking a question should help, and it probably already did [LW(p) · GW(p)]). If this is not OK, this is a disincentive for new people from getting publicly curious.
Edit: And just a few minutes after this, someone strong-downvoted again, back to 0. Possibly a strong dislike for violence in thought experiments? It does seem to be going out of style.
Replies from: Dagon↑ comment by Dagon · 2021-09-15T20:26:47.043Z · LW(p) · GW(p)
I downvoted (to 0, IIRC, no need to be punitive). Aanchpop, I don't want to discourage curiosity or asking questions, and I welcome further posts by you! But I don't want something that's been covered pretty thoroughly to show up as highly-voted, when it's not particularly clear or insightful.
At the very least, summarizing the two common approaches, or whatever thoughts you identify as contradictory/problematic in your analysis, would help other people who haven't seen similar problems understand what ground you're exploring.