stephen: If we had a full understanding of fundamental physics then the only other a priori assumption we should need to derive the Born rule should be this: We aren't special. Our circumstances are typical. In other words: it is possible that at a fundamental physical level there is no Born rule and no reason one should expect a Born rule. But just by some fantastic coincidence, *our* little branch has followed the born rule all this time. In fact, we should expect it to stop following the Born rule immediately, for the same reason someone who's just won the lottery doesn't expect to win again next time. It's not physically impossible for us to be this lucky, but it's not physically impossible for an egg to unscramble itself either.

Fundamental physics + eggs don't unscramble + anthropic principle should give you the Born rule. If it doesn't then physicists aren't done yet.