Best-of-Both-Worlds Fairness in Committee Voting
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The paradigm of best-of-both-worlds advocates an approach that achieves desirable properties both ex-ante and ex-post. We initiate a best-of-both-worlds fairness perspective for the important social choice setting of approval-based committee voting. To this end, we formalize a hierarchy of ex-ante properties including Individual Fair Share (IFS) and its strengthening Group Fair Share (GFS). We establish their relations with well-studied ex-post concepts such as extended justified representation (EJR) and proportional justified representation (PJR). Our central result is a polynomial-time algorithm that simultaneously satisfies ex-post EJR and ex-ante GFS. Our algorithm uses as a subroutine the first phase of the well-known Method of Equal Shares class of rules.
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