提出可论证的多胜者投票机制，让选民表达有争议的偏好。
Multi-Winner Voting with Argumentative Ballots
- 用可反驳的论证替代传统批准票，增强表达力。
- 仅能始终满足基础代表权，强代表权无法保证。
- 方法形式化验证，适合制度设计与公平性研究者。
我们提出多胜者投票中的可论证选票（MVArg）并研究其理论性质。作为概念贡献，我们将批准选票推广为可论证选票，使选民能够表达对候选人的可反驳偏好。相应地，我们推广了选民凝聚性和公正代表性的公理（JR、PJR、EJR）。作为理论贡献，我们建立了若干关键结果：第一，MVArg比传统的多胜者批准投票（MV）更富表达力；第二，我们的凝聚性与公正代表定义是MV中对应概念的保守推广；第三，MVArg下的JR公理总可满足，而PJR和EJR的对应形式则不一定；第四，验证一个获胜集合是否满足MVArg下的JR已是coNP难问题，但此类获胜集合可在多项式时间内构造。所有定义、命题、引理与定理均在Lean 4中形式化并机械验证。
原文摘要 · Abstract (English)
We introduce multi-winner voting with argumentative ballots (MVArg) and investigate theoretical properties. As our conceptual contribution, we generalise approval ballots to argumentative ballots, thereby allowing voters to express defeasible preferences over candidates. We accordingly generalise voter cohesion and justified representation axioms JR, PJR and EJR. As our theoretical contribution, we establish several key results. First, MVArg is strictly more expressive than multi-winner voting with approval ballots (MV). Second, our notions of cohesion and justified representation are conservative generalisations of their counterparts in MV. Third, the MVArg counterpart of JR can always be satisfied, whereas the counterparts of PJR and EJR cannot always be. Fourth, although verifying whether a winner set satisfies the MVArg counterpart of JR is already coNP-hard, such a winner set can be constructed in polynomial time. All definitions, propositions, auxiliary lemmas and theorems have been formalised and mechanically checked in Lean 4.
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