Multi-winner voting plays a crucial role in selecting representative committees based on voter preferences. Previous research has predominantly focused on single-stage voting rules, which are susceptible to manipulation during preference collection. In order to mitigate manipulation and increase the cost associated with it, we propose the introduction of multiple stages in the voting procedure, leading to the development of a unified framework of multi-stage multi-winner voting rules. To shed light on this framework of voting methods, we conduct an axiomatic study, establishing provable conditions for achieving desired axioms within our model. Our theoretical findings can serve as a guide for the selection of appropriate multi-stage multi-winner voting rules.

翻译：多胜者投票在选择基于选民偏好的代表性委员会中起着关键作用。以往研究主要聚焦于单阶段投票规则，这类规则在偏好收集过程中易受操纵。为减少操纵行为并提高其成本，我们提出在投票流程中引入多阶段机制，进而发展出多阶段多胜者投票规则的统一框架。为阐明此类投票方法框架，我们进行了公理化研究，在模型中建立了实现理想公理的可证明条件。我们的理论发现可作为选择合适多阶段多胜者投票规则的指导依据。