  Probabilities in quantum theory are traditionally given by Born's rule as the
expectation values of projection operators. Here it is shown that Born's rule
is insufficient in universes so large that they contain identical multiple
copies of observers, because one does not have definite projection operators to
apply. Possible replacements for Born's rule include using the expectation
value of various operators that are not projection operators, or using various
options for the average density matrix of a region with an observation. The
question of what replacement to use is part of the measure problem in
cosmology.
