  There is a compelling intellectual case for exploring whether purely unitary
quantum theory defines a sensible and scientifically adequate theory, as
Everett originally proposed. Many different and incompatible attempts to define
a coherent Everettian quantum theory have been made over the past fifty years.
However, no known version of the theory (unadorned by extra ad hoc postulates)
can account for the appearance of probabilities and explain why the theory it
was meant to replace, Copenhagen quantum theory, appears to be confirmed, or
more generally why our evolutionary history appears to be Born-rule typical.
This article reviews some ingenious and interesting recent attempts in this
direction by Wallace, Greaves, Myrvold and others, and explains why they don't
work. An account of one-world randomness, which appears scientifically
satisfactory, and has no many-worlds analogue, is proposed. A fundamental
obstacle to confirming many-worlds theories is illustrated by considering some
toy many-worlds models. These models show that branch weights can exist without
having any role in either rational decision-making or theory confirmation, and
also that the latter two roles are logically separate. Wallace's proposed
decision theoretic axioms for rational agents in a multiverse and claimed
derivation of the Born rule are examined. It is argued that Wallace's strategy
of axiomatizing a mathematically precise decision theory within a fuzzy
Everettian quasiclassical ontology is incoherent. Moreover, Wallace's axioms
are not constitutive of rationality either in Everettian quantum theory or in
theories in which branchings and branch weights are precisely defined. In both
cases, there exist coherent rational strategies that violate some of the
axioms.
