Efficiency in multiwinner voting is most naturally captured by Pareto-optimality (PO), yet this notion is computationally and structurally difficult to handle. We therefore study fractional Pareto-optimality (fPO), under which a committee may not be dominated even by a fractional committee, i.e., any convex combination of committees. fPO turns out to be a natural refinement of PO as it retains exactly those Pareto-optimal committees whose efficiency is robust under uniform cloning of candidates. Furthermore, fPO committees are guaranteed to exist and have strong structural properties. We present a characterization of fPO in terms of weighted utilitarian welfare maximization, which yields a polynomial-time algorithm for verifying fPO and shows that the set of fPO committees satisfies committee monotonicity and is connected under single-candidate swaps. Analyzing welfarist rules through the lens of fPO, we further uncover an incompatibility between fPO and equality-oriented objectives. Most notably, we show that proportional approval voting (PAV) violates fPO in the approval setting. We close by pinpointing preference domains, including various one-dimensional ones, on which PO and fPO collapse into one notion.

翻译：多人投票中的效率最自然地通过帕累托最优性（PO）来刻画，然而这一概念在计算和结构上难以处理。因此，我们研究分数帕累托最优性（fPO），在该概念下，一个委员会即使不能被分数委员会（即委员会的任意凸组合）所支配。fPO被证明是PO的一个自然精炼，因为它恰好保留了那些在候选人的均匀克隆下效率具有鲁棒性的帕累托最优委员会。此外，fPO委员会保证存在并具有强结构性质。我们通过加权功利社会福利最大化给出了fPO的一个刻画，该刻画导出了检验fPO的多项式时间算法，并表明fPO委员会集合满足委员会单调性且在单一候选人交换下是连通的。通过fPO的视角分析功利主义规则，我们进一步揭示了fPO与平等导向目标之间的不相容性。最值得注意的是，我们证明比例批准投票（PAV）在批准设置下违反了fPO。最后，我们确定了偏好域（包括各种一维偏好域）上PO与fPO合并为同一概念的情况。