We revisit the recent breakthrough result of Gkatzelis et al. on (single-winner) metric voting, which showed that the optimal distortion of 3 can be achieved by a mechanism called Plurality Matching. The rule picks an arbitrary candidate for whom a certain candidate-specific bipartite graph contains a perfect matching, and thus, it is not neutral (i.e, symmetric with respect to candidates). Subsequently, a much simpler rule called Plurality Veto was shown to achieve distortion 3 as well. This rule only constructs such a matching implicitly but the winner depends on the order that voters are processed, and thus, it is not anonymous (i.e., symmetric with respect to voters). We provide an intuitive interpretation of this matching by generalizing the classical notion of the (proportional) veto core in social choice theory. This interpretation opens up a number of immediate consequences. Previous methods for electing a candidate from the veto core can be interpreted simply as matching algorithms. Different election methods realize different matchings, in turn leading to different sets of candidates as winners. For a broad generalization of the veto core, we show that the generalized veto core is equal to the set of candidates who can emerge as winners under a natural class of matching algorithms reminiscent of Serial Dictatorship. Extending these matching algorithms into continuous time, we obtain a highly practical voting rule with optimal distortion 3, which is also intuitive and easy to explain: Each candidate starts off with public support equal to his plurality score. From time 0 to 1, every voter continuously brings down, at rate 1, the support of her bottom choice among not-yet-eliminated candidates. A candidate is eliminated if he is opposed by a voter after his support reaches 0. On top of being anonymous and neutral, this rule satisfies many other axioms desirable in practice.

翻译：我们重新审视了Gkatzelis等人近期在（单胜者）度量投票领域取得的突破性成果，该成果表明通过一种名为Plurality Matching的机制可实现最优失真度3。该规则选择任意一名候选人，其对应的特定候选人二部图存在完美匹配，因此该规则非中性（即对候选人不对称）。随后，一种更简单的规则Plurality Veto被证明也能实现失真度3。该规则仅隐式构造了此类匹配，但胜者取决于选民的处理顺序，因此非匿名（即对选民众不对称）。我们通过推广社会选择理论中经典的（比例）否决核概念，为这种匹配提供了直观解释。该解释衍生出若干直接推论：先前从否决核中选举候选人的方法可简单理解为匹配算法，不同选举方法实现不同匹配，进而产生不同的胜者候选集。针对否决核的广泛泛化，我们证明广义否决核等于在类似序列独裁的自然匹配算法类中可能胜出的候选者集合。将这些匹配算法延伸至连续时间，我们获得一种具有最优失真度3的高度实用投票规则，该规则直观易懂：每位候选人初始获得等同于其得票率的公开支持度。在时间0至1区间内，每位选民以速率1持续降低其未淘汰候选人中最低选择者的支持度。若候选人支持度降至零后仍遭选民反对，则遭淘汰。该规则除具备匿名性与中性外，还满足多项实践中所需的良好公理性质。