发表机构
Massachusetts Institute of Technology; Harvard University（麻省理工学院; 哈佛大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究分析带加性效用的参与式预算与委员会选举中各类正当代表制公理的计算复杂性，证明满足FJR是强NP难问题，扩展了扩展认可规则并证明其满足PJR，指出需全新投票规则突破现有界限。
AI 中文摘要
我们研究在具有加性效用的参与式预算和委员会选举中满足比例代表制的计算复杂性，具体包括比例代表制（PJR）、扩展比例代表制（EJR）和完全正当代表制（FJR）。首先，我们针对固定数量的选民或选民类型，给出了这些公理的复杂性的完整图景。其次，我们证明即使对于效用被小常数上界约束的委员会选举，满足FJR也是难解的，这给出了正当代表制公理的首个强NP难结果。第三，我们将扩展认可规则（Expanding Approvals Rule）扩展到带加性效用的委员会选举，并证明其满足PJR。最后，我们证明没有任何顺序投票规则能超越已知的正面结果，因此需提出全新的、本质上不同的投票规则才能突破这些界限。除理论价值外，我们的结果具有实践意义，因为带加性效用的多获胜者投票近期在在线审议和现实参与式预算中日益受到重视。
英文摘要
We study the computational complexity of satisfying proportional representation -- in particular proportional, extended, and fully justified representation (PJR, EJR, and FJR) -- in participatory budgeting and committee elections with additive utilities. First, we give a complete picture of the complexity of the axioms for a constant number of voters or voter types. Second, we show that even for committee elections with integer utilities bounded above by a small constant, satisfying FJR is intractable, giving the first strong NP-hardness result for a justified representation axiom. Third, we extend the Expanding Approvals Rule to committee elections with additive utilities and show that it satisfies PJR. Lastly, we show that no sequential voting rule can improve on the known positive result, thus proving that novel, substantially different voting rules are needed to surpass these boundaries. Beyond their theoretical merit, our results carry practical importance, as multi-winner voting with additive utilities has recently been gaining prominence in online deliberation and real-world participatory budgeting.
