提出新比例代表制标准,兼顾公平性与可计算性。
Full Proportional Justified Representation
- 定义新标准FPJR:基于部分同意与集体效用的组合要求
- 证明高效算法如等额分配规则满足FPJR,而PAV可能违反
- 兼具PJR的兼容性优势与对完美代表性的更强保障
在多赢批准投票中,构建一个能按比例代表选民批准票的委员会至关重要。现有比例代表制(JR)有多种定义方式,分别基于‘凝聚力’(C1/C2)和‘代表性’(R1/R2)的不同组合。本文研究组合(C2)-(R1),提出全比例公正代表(FPJR)。我们发现,多个比例性公理(如可定价性、完美代表)蕴含FPJR和PJR,但不蕴含EJR。此外,高效的贪婪蒙罗规则和等额分配法满足FPJR,这是其优于传统FJR的关键优势。然而,比例批准投票(PAV)规则可能违反FPJR,说明EJR与FPJR互不包含。
原文摘要 · Abstract (English)
In multiwinner approval voting, forming a committee that proportionally represents voters' approval ballots is an essential task. The notion of justified representation (JR) demands that any large "cohesive" group of voters should be proportionally "represented". The "cohesiveness" is defined in different ways; two common ways are the following: (C1) demands that the group unanimously approves a set of candidates proportional to its size, while (C2) requires each member to approve at least a fixed fraction of such a set. Similarly, "representation" have been considered in different ways: (R1) the coalition's collective utility from the winning set exceeds that of any proportionally sized alternative, and (R2) for any proportionally sized alternative, at least one member of the coalition derives less utility from it than from the winning set. Three of the four possible combinations have been extensively studied: (C1)-(R1) defines Proportional Justified Representation (PJR), (C1)-(R2) defines Extended Justified Representation (EJR), (C2)-(R2) defines Full Justified Representation (FJR). All three have merits, but also drawbacks. PJR is the weakest notion, and perhaps not sufficiently demanding; EJR may not be compatible with perfect representation; and it is open whether a committee satisfying FJR can be found efficiently. We study the combination (C2)-(R1), which we call Full Proportional Justified Representation (FPJR). We investigate FPJR's properties and find that it shares PJR's advantages over EJR: several proportionality axioms (e.g. priceability, perfect representation) imply FPJR and PJR but not EJR. We also find that efficient rules like the greedy Monroe rule and the method of equal shares satisfy FPJR, matching a key advantage of EJR over FJR. However, the Proportional Approval Voting (PAV) rule may violate FPJR, so neither of EJR and FPJR implies the other.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。