发表机构
Kyoto University; Nagoya University（京都大学; 名古屋大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出带论证选票的多获胜者投票（MVArg），推广了相关公理，证明其表达能力更强，部分公理总能满足、部分不能，且相关验证问题的复杂度与构造性。
AI 中文摘要
我们提出带论证选票的多获胜者投票（MVArg）并研究其理论性质。作为概念贡献，我们将认可选票推广为论证选票，使投票者能表达对候选人的可废止偏好；据此，我们推广了投票者凝聚力及正当代表性公理JR、PJR、EJR。作为理论贡献，我们得到若干关键结果：第一，MVArg的表达能力严格强于带认可选票的多获胜者投票（MV）；第二，我们的凝聚力与正当代表性概念是MV对应概念的保守推广；第三，MVArg的JR对应概念总能满足，而PJR、EJR的对应概念并非总能满足；第四，验证某获胜者集合是否满足MVArg的JR对应概念已是coNP-难，但该获胜者集合可在多项式时间内构造。所有定义、命题、辅助引理及定理均已在Lean 4中形式化并经机械核验。
英文摘要
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.
CommentsCorrected Example 1, reflected the update to page 6's counts of winner sets proving axioms for the robust h. No definitions, propositions, lemmas, theorems are affected
