  The best-of-both-worlds paradigm advocates an approach that achieves
desirable properties both ex-ante and ex-post. We launch a best-of-both-worlds
fairness perspective for the important social choice setting of approval-based
committee voting. To this end, we initiate work on ex-ante proportional
representation properties in this domain and formalize a hierarchy of notions
including Individual Fair Share (IFS), Unanimous Fair Share (UFS), Group Fair
Share (GFS), and their stronger variants. We establish their compatibility with
well-studied ex-post concepts such as extended justified representation (EJR)
and fully justified representation (FJR). Our first main result is a
polynomial-time algorithm that simultaneously satisfies ex-post EJR, ex-ante
GFS and ex-ante Strong UFS. Subsequently, we strengthen our ex-post guarantee
to FJR and present an algorithm that outputs a lottery which is ex-post FJR and
ex-ante Strong UFS, but does not run in polynomial time.
