Approval-Based Apportionment: Like Portioning, Approximately like Committee Voting

2026-08-27

AI Summary

研究了基于批准的分配问题，通过分析不同比例公理的关系及Lindahl价格性与PAV得分近似最优性的等价性，揭示了该问题介于委员会选举和份额划分之间。

Abstract

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.

Problem

• approval-based apportionment
• proportionality axioms
• core stability

Innovation

• Approval-based apportionment
• Proportionality axioms
• Lindahl priceability
• PAV score
• Portioning