  Realist, no-collapse interpretations of quantum mechanics, such as Everett's,
face the probability problem: how to justify the norm-squared (Born) rule from
the wavefunction alone. While any basis-independent measure can only be
norm-squared (due to the Gleason-Busch Theorem) this fact conflicts with
various popular, non-wavefunction-based phenomenological measures - such as
observer, outcome or world counting - that are frequently demanded of
Everettians. These alternatives conflict, however, with the wavefunction
realism upon which Everett's approach rests, which seems to call for an
objective, basis-independent measure based only on wavefunction amplitudes. The
ability of quantum probabilities to destructively interfere with each other,
however, makes it difficult to see how probabilities can be derived solely from
amplitudes in an intuitively appealing way. I argue that the use of algorithmic
probability can solve this problem, since the objective, single-case
probability measure that wavefunction realism demands is exactly what
algorithmic information theory was designed to provide. The result is an
intuitive account of complex-valued amplitudes, as coefficients in an optimal
lossy data compression, such that changes in algorithmic information content
(entropy deltas) are associated with phenomenal transitions.
