  It is usually assumed that the quantum state is sufficient for deducing all
probabilities for a system. This may be true when there is a single observer,
but it is not true in a universe large enough that there are many copies of an
observer. Then the probability of an observation cannot be deduced simply from
the quantum state (say as the expectation value of the projection operator for
the observation, as in traditional quantum theory). One needs additional rules
to get the probabilities. What these rules are is not logically deducible from
the quantum state, so the quantum state itself is insufficient for deducing
observational probabilities. This is the measure problem of cosmology.
