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Tim_Tyler comments on The Dilemma: Science or Bayes? - Less Wrong
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According to:
http://www.hedweb.com/everett/everett.htm#believes
...most "leading cosmologists and other quantum field theorists" thought that the "Many-Worlds Interpretation was correct 10 years ago.
Supporters tend to cite not Solomonoff induction, but simply Occam's razor.
Solomonoff induction is simply an attempt to formalise Occam's razor around an impractical theoretical model of serial computation.