  A defence is offered of a version of the branch-counting rule for probability
in the Everett interpretation (otherwise known as many-worlds interpretation)
of quantum mechanics that both depends on the state and is continuous in the
norm topology on Hilbert space. The well-known branch-counting rule, for
realistic models of measurements, in which branches are defined by decoherence
theory, fails this test. The new rule hinges on the use of decoherence theory
in defining branching structure, and specifically decoherent histories theory.
On this basis ratios of branch numbers are defined, free of any convention.
They agree with the Born rule, and deliver a notion of objective probability
similar to na\"ive frequentism, save that the frequencies of outcomes are not
confined to a single world at different times, but spread over worlds at a
single time. Nor is it ad hoc: it is recognizably akin to the combinatorial
approach to thermodynamic probability, as introduced by Boltzmann in 1879. It
is identical to the procedure followed by Planck, Bose, Einstein and Dirac in
defining the equilibrium distribution of the Bose-Einstein gas. It also
connects in a simple way with the decision-theory approach to quantum
probability.
