This paper is an axiomatic study of consistent approval-based multi-winner
rules, i.e., voting rules that select a fixed-size group of candidates based on
approval ballots. We introduce the class of counting rules and provide an
axiomatic characterization of this class based on the consistency axiom.
Building upon this result, we axiomatically characterize three important
consistent multi-winner rules: Proportional Approval Voting, Multi-Winner
Approval Voting and the Approval Chamberlin--Courant rule. Our results
demonstrate the variety of multi-winner rules and illustrate three different,
orthogonal principles that multi-winner voting rules may represent: individual
excellence, diversity, and proportionality.

本文是对一种称为 “基于批准的多赢家规则” 的投票规则进行的公理化研究，介绍了计数规则，提供了基于一致性公理的这个类别的公理特征描述，并基于此，公理化刻画了三种重要的一致性多赢家规则：比例批准投票、多赢家批准投票和批准的钦定 -- 卡伦特规则。我们的研究结果展示了多赢家规则的种类和三个不同的正交原则，它们是：个人品质、多样性和比例性。

一致的基于批准的多获胜者规则

Consistent Approval-Based Multi-Winner Rules

We consider approval-based committee voting, i.e. the setting where each
voter approves a subset of candidates, and these votes are then used to select
a fixed-size set of winners (committee). We propose a natural axiom for this
setting, which we call justified representation (JR). This axiom requires that
if a large enough group of voters exhibits agreement by supporting the same
candidate, then at least one voter in this group has an approved candidate in
the winning committee. We show that for every list of ballots it is possible to
select a committee that provides JR. However, it turns out that several
prominent approval-based voting rules may fail to output such a committee. In
particular, while Proportional Approval Voting (PAV) always outputs a committee
that provides JR, Reweighted Approval Voting (RAV), a tractable approximation
to PAV, does not have this property. We then introduce a stronger version of
the JR axiom, which we call extended justified representation (EJR), and show
that PAV satisfies EJR, while other rules we consider do not; indeed, EJR can
be used to characterize PAV within the class of weighted PAV rules. We also
consider several other questions related to JR and EJR, including the
relationship between JR/EJR and core stability, and the complexity of the
associated algorithmic problems.

研究了基于批准的委员会投票机制，提出了正当代表公理和扩展正当代表公理，研究了多种规则是否符合这些公理，分析了核稳定性和算法问题。