I had a very similar reaction when I first read Everett’s thesis as well (after having previously read Eliezer’s quantum physics sequence). I reproduced Everett’s proof in “Multiple Worlds, One Universal Wave Function,” precisely because I felt like it did dissolve a lot of the problem—and I also reference a couple of other similar proofs from more recent authors in that paper which you might find interesting; see references 11 and 18.
I also once showed Everett’s proof to Nate Soares (who can perhaps serve as a stand-in for Eliezer here), who had a couple of objections. IIRC, he thought that it didn’t fully dissolve the problem because it a) assumed that the Born rule had to only be a function of the amplitude and b) didn’t really answer the anthropic question of why we see anything like the Born rule in the first place, only the mathematical question of why, if we see any amplitude-based rule, it has to be the squared amplitude.
Imo, I think b) is a correct objection, in the sense that I think it’s literally true, but also a bit unfair, since I think you could level a similar objection against essentially any physical law.
I had a very similar reaction when I first read Everett’s thesis as well (after having previously read Eliezer’s quantum physics sequence). I reproduced Everett’s proof in “Multiple Worlds, One Universal Wave Function,” precisely because I felt like it did dissolve a lot of the problem—and I also reference a couple of other similar proofs from more recent authors in that paper which you might find interesting; see references 11 and 18.
I also once showed Everett’s proof to Nate Soares (who can perhaps serve as a stand-in for Eliezer here), who had a couple of objections. IIRC, he thought that it didn’t fully dissolve the problem because it a) assumed that the Born rule had to only be a function of the amplitude and b) didn’t really answer the anthropic question of why we see anything like the Born rule in the first place, only the mathematical question of why, if we see any amplitude-based rule, it has to be the squared amplitude.
I think b) is what I always assumed was meant by the Born rule being called mysterious?
Imo, I think b) is a correct objection, in the sense that I think it’s literally true, but also a bit unfair, since I think you could level a similar objection against essentially any physical law.