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Jack comments on A note on the description complexity of physical theories - Less Wrong
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There's a useful heuristic to solve tricky questions about "truths" and "beliefs": reduce them to questions about decisions and utilities. For example, the Sleeping Beauty problem is very puzzling if you insist on thinking in terms of subjective probabilities, but becomes trivial once you introduce any payoff structure. Maybe we could apply this heuristic here? Believing in one formulation of a theory over a different equivalent formulation isn't likely to win a Bayesian reasoner many dollars, no matter what observations come in.
Except the whole quantum suicide thing does create payoff structures. In determining weather or not to play a game of Quantum Russian Roulette you take your estimated winnings for playing if MWI and Quantum immortality is true and your estimated winnings if MWI or Quantum immortality is false and weigh them according to the probability you assign each theory.
(ETA: But this seems to be a quirky feature of QM interpretation, not a feature of empirically equivalent theories generally.)
(ETA 2: And it is a quirky feature of QM interpretation because MWI+Quantum Immortality is empirically equivalent to single world theories is a really quirky way.)
IMO quantum suicide/immortality is so mysterious that it can't support any definite conclusions about the topic we're discussing. I'm beginning to view it as a sort of thread-killer, like "consciousness". See a comment that mentions QI, collapse the whole thread because you know it's not gonna make you happier.
I agree that neither we nor anyone else do a good job discussing it. It seems like a pretty important issue though.