基于认可的席位分配：类似分额分配，近似于委员会投票
Approval-Based Apportionment: Like Portioning, Approximately like Committee Voting
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中文总结 AI 辅助
该研究探讨基于认可的席位分配，证明其部分比例公理等价性，揭示其与分额分配的关联，认为其更接近分额分配，为委员会选举近似关系推测提供有效场景。
中文摘要 AI 辅助
我们研究基于认可的席位分配（approval-based apportionment），这是一种委员会选举的变体，其中候选人（“政党”）可被多次选中。我们证明比例性公理EJR、EJR+和FJR是等价的，PJR、PJR+和FPJR也是等价的；林达尔定价性（Lindahl priceability，一种隐含核心稳定性的公理）与比例认可投票（proportional approval voting，PAV）得分下的近似最优性概念等价；局部PAV最优的委员会是可定价的。基于认可的席位分配（候选人获得整数个席位）介于委员会选举（0或1个席位）和分额分配（分数个席位）之间。我们通过构造将公理从席位分配提升至分额分配并保留它们之间的蕴含关系，在形式上连接了分额分配与席位分配。我们提出的多个席位分配公理间的蕴含关系从分额分配视角来看是自然的，这使我们认为席位分配比委员会选举更接近分额分配。这些蕴含关系在委员会选举中均不成立，但有几个可近似扩展，这使得席位分配成为在基于认可的委员会选举中推测近似关系的有效场景。
英文摘要
We study approval-based apportionment, a variant of committee elections in which candidates ("parties") can be selected several times. We show that the proportionality axioms EJR, EJR+, and FJR coincide, and so do PJR, PJR+, and FPJR; that Lindahl priceability, an axiom implying core stability, is equivalent to a notion of approximate optimality with respect to the proportional approval voting (PAV) score; and that locally PAV-optimal committees are priceable. Approval-based apportionment (where a candidate receives an integer number of seats) lies between committee elections (zero or one seat) and portioning (a fractional number of seats). We formally connect portioning and apportionment by giving a construction that lifts axioms from apportionment to portioning and preserves implications between them. Several of our new implications between apportionment axioms are natural from a portioning perspective, leading us to believe that apportionment sits closer to portioning than to committee elections. None of them holds in committee elections, but several extend approximately, which makes apportionment a fruitful setting for conjecturing approximate relationships in approval-based committee elections.
