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.

翻译：双赢范式倡导一种同时实现事前和事后理想属性的方法。我们将双赢公平视角引入基于批准的委员会投票这一重要社会选择场景。为此，我们在该领域率先研究事前比例代表性属性，并形式化了一个包含个人公平份额、一致公平份额、群体公平份额及其更强变体的概念层次。我们证明了这些概念与广泛研究的后验概念（如扩展正当代表性（EJR）和完全正当代表性（FJR））的兼容性。我们第一个主要结果是一个多项式时间算法，可同时满足后验EJR、事前GFS和事前强UFS。随后，我们将后验保证强化为FJR，并提出了一个输出后验FJR和事前强UFS的抽签算法，但该算法不具备多项式时间复杂度。