In party-approval multiwinner elections the goal is to allocate the seats of a fixed-size committee to parties based on the approval ballots of the voters over the parties. In particular, each voter can approve multiple parties and each party can be assigned multiple seats. Two central requirements in this setting are proportional representation and strategyproofness. Intuitively, proportional representation requires that every sufficiently large group of voters with similar preferences is represented in the committee. Strategyproofness demands that no voter can benefit by misreporting her true preferences. We show that these two axioms are incompatible for anonymous party-approval multiwinner voting rules, thus proving a far-reaching impossibility theorem. The proof of this result is obtained by formulating the problem in propositional logic and then letting a SAT solver show that the formula is unsatisfiable. Additionally, we demonstrate how to circumvent this impossibility by considering a weakening of strategy\-proofness which requires that only voters who do not approve any elected party cannot manipulate. While most common voting rules fail even this weak notion of strategyproofness, we characterize Chamberlin--Courant approval voting within the class of Thiele rules based on this strategyproofness notion.
翻译:在政党批准的多赢选举中,目标是根据选民对政党的核准选票,将固定规模委员会的席位分配给政党。特别是,每个选民可以批准多个政党,每个政党可以分配多个席位。在这一背景下,有两个核心要求是比例代表制和战略防守性。直观地说,比例代表制要求每个足够多的具有类似偏好的选民群体在委员会中都有代表。战略防守性要求任何选民不能通过错误报告其真实偏好而受益。我们表明,这两个轴心不符合匿名政党核准的多赢多赢多赢选举规则,从而证明一个影响深远的不可能的理论。通过用假设逻辑提出问题,然后让沙特德士古公司解决问题者表明公式是不满意的,就能够证明这一结果的证据。此外,我们证明如何通过考虑削弱战略防偏差,要求只有不认可任何当选政党的选民才能操纵。尽管大多数常见的投票规则甚至不能满足这一薄弱的战略防偏差概念,但我们将安倍的核准票标定在基于这一战略概念的提埃里规则范围内。