  It is often objected that the Everett interpretation of QM cannot make sense
of quantum probabilities, in one or both of two ways: either it can't make
sense of probability at all, or it can't explain why probability should be
governed by the Born rule. David Deutsch has attempted to meet these
objections. He argues not only that rational decision under uncertainty makes
sense in the Everett interpretation, but also that under reasonable
assumptions, the credences of a rational agent in an Everett world should be
constrained by the Born rule. David Wallace has developed and defended
Deutsch's proposal, and greatly clarified its conceptual basis. In particular,
he has stressed its reliance on the distinguishing symmetry of the Everett
view, viz., that all possible outcomes of a quantum measurement are treated as
equally real. The argument thus tries to make a virtue of what has usually been
seen as the main obstacle to making sense of probability in the Everett world.
In this note I outline some objections to the Deutsch-Wallace argument, and to
related proposals by Hilary Greaves about the epistemology of Everettian QM.
(In the latter case, my arguments include an appeal to an Everettian analogue
of the Sleeping Beauty problem.) The common thread to these objections is that
the symmetry in question remains a very significant obstacle to making sense of
probability in the Everett interpretation.
