AI 中文总结
本文提出满足完全正当代表制的多项式时间贪心正当候选人规则变体，解决了高效计算FJR委员会的开放问题，并否定回答了MES委员会扩展至FJR的相关开放问题。
AI 中文摘要
在基于认可的多获胜者投票中，选民提交认可选票，以此选出规模固定为k的委员会，与单获胜者投票相比，这能让少数群体也能在委员会中得到代表，因此多获胜者投票最理想的目标之一是满足比例代表制。本文提出了贪心正当候选人规则的一种变体，该变体满足完全正当代表制（Full Justified Representation，FJR）的概念，且可在多项式时间内计算，回答了是否总能高效计算出FJR委员会的开放问题；此外，我们否定回答了MES返回的委员会是否总能被扩展以满足FJR的开放问题。
英文摘要
In approval-based multiwinner voting, voters submit an approval ballot on which basis a committee of fixed size $k$ has to be selected. Compared to single-winner voting this makes it possible to represent minorities in the selection of the committee as well. Thus, one of the most desirable goals of multiwinner voting is to satisfy proportional representation. In this paper we propose a variant of the Greedy Justified Candidate rule that satisfy the notion of Full Justified Representation (FJR). This variant can be computed in polynomial time answering the open question of whether an FJR committee can always be computed efficiently. Additionally, we answer an open question whether committees returned by MES can always be extended in a way to satisfy FJR negatively.
