  In the modern quantum mechanics of cosmology observers are physical systems
within the universe. They have no preferred role in the formulation of the
theory nor in its predictions of third person probabilities of what occurs.
However, observers return to importance for the prediction of first person
probabilities for what we observe of the universe: What is most probable to be
observed is not necessarily what is most probable to occur. This essay reviews
the basic framework for the computation of first person probabilities in
quantum cosmology starting with an analysis of very simple models. It is shown
that anthropic selection is automatic in this framework, because there is no
probability for us to observe what is where we cannot exist. First person
probabilities generally favor larger universes resulting from inflation where
there are more places for us to be. In very large universes it is probable that
our observational situation is duplicated elsewhere. The calculation of first
person probabilities then requires a specification of whether our particular
situation is assumed to be typical of all the others. It is the combination of
the model of the observational situation, including this typicality assumption,
and the third person theory which is tested by observation. We conclude with a
discussion of the first person predictions of cosmological observables such as
the cosmological constant and features of the primordial density fluctuations,
in the no-boundary quantum state of the universe and a dynamical theory in
which these are allowed to vary.
