In approval-based multiwinner voting, Pareto optimality is used as an axiom capturing efficiency of committees. We study the structure of the space of Pareto optimal committees in restricted domains and in general by investigating the monotonicity and reconfigurability of such committees. For the Candidate Interval and Voter Interval domains, we propose the Single Dominance Only property, which provides a simple characterization of Pareto optimality, and show that Pareto optimal committees satisfy committee monotonicity using this property. Further, we show that, for the above domains, any Pareto optimal committee can be reconfigured into any other Pareto optimal target committee without using auxiliary candidates, meaning that the candidates in the starting but not the target committee can be replaced by candidates in the target but not the starting committee one by one while preserving Pareto optimality at every step. In addition, we adapt a polynomial-time algorithm for finding a committee satisfying EJR+, a proportionality axiom, such that it also satisfies Pareto optimality, for the above domains. We further describe a polynomial-time algorithm for counting the number of Pareto optimal committees for voting instances satisfying Voter Interval, and give a proof idea for its correctness. For the unrestricted domain, we explain the challenges of proving committee monotonicity and reconfigurability. We provide an example in which the distance of two committees in the Pareto optimality reconfiguration graph exceeds the distance proven for the above domains, and outline an approach toward showing the connectedness of the graph.

翻译：在审批制多赢者投票中，帕累托最优性被用作刻画委员会效率的公理。我们通过研究帕累托最优委员会在受限领域和一般情况下的单调性与可重构性，探索其结构空间。针对候选区间与选民区间领域，我们提出"单一支配性"属性——该属性为帕累托最优性提供了简洁的刻画，并证明在此属性下帕累托最优委员会满足委员会单调性。进一步研究表明，在上述领域内，任意帕累托最优委员会可在不使用辅助候选人的情况下重构为其他任意帕累托最优目标委员会，这意味着起始委员会中非目标委员会的候选人可逐个被目标委员会中非起始委员会的候选人替换，且每一步均保持帕累托最优性。此外，我们针对上述领域改进了一种多项式时间算法，用于寻找同时满足帕累托最优性与比例性公理EJR+的委员会。我们还提出了针对满足选民区间投票实例的帕累托最优委员会计数多项式时间算法，并给出其正确性的证明思路。对于无约束领域，我们阐释了证明委员会单调性与可重构性面临的挑战。通过实例展示，帕累托最优性重构图中两委员会距离可能超过上述领域已证明的界值，并勾勒出证明该图连通性的研究路径。