Goddamn that is a good paper. Some of the questions have been partially answered since then, though it would take me too long now to write about that. I love how it shows that philosophy is not divorceable from quantum mechanics (or, really, any human endeavor).
I’ve been thinking a lot about probability lately, in this context and others, and how it’s a flawed but useful tool.
For N sufficiently large and |c+| ≠ |c−|, it can be shown that the vast majority of the 2N realized observers (i.e., weighting each distinct observer equally) see an outcome which is highly unlikely according to the usual probability rules. Note that counting of possible outcomes depends only on combinatorics and is independent of c±. As N → ∞, for all values of c± (excluding exactly zero), almost all of the realized observers find nearly equal number of + and − spins: there are many more outcomes of the form, e.g., (+ + − + − · · · + − − +) with roughly equal number of +’s and −’s than with many more of one than the other. This had to be the case, because counting of outcomes is independent of the values of c±, leading to a symmetry between + and − outcomes in the combinatorics. In contrast, the Born rule predicts that the relative number of + and − outcomes depends on |c±| . In the large N limit almost all (distinct) observers experience outcomes that strongly disfavor the Born probability rule: almost all of the physicists in the multiverse see experimental violation of the Born rule. Or: almost none of the physicists in the multiverse see outcomes consistent with the Born rule.
That’s something I’d realized myself, though I’d not put it quite that formally. Reality is essentially broken, because no matter how you think about it, using the best tools we have, there is something strange going on: either causality is false (this appears to be true in this universe), or you lose locality. And in most formulations of QM probability is completely wacky in irreconcilable ways! And it just seems to be the way the universe works.