发表机构
Boston University（波士顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对认可选举中黑尔核心是否存在的开放问题，证明选民弃权最多两名候选人时黑尔核心必存在，提出基于缺失集的确定性规则并通过符号证明确立其有效性。
AI 中文摘要
若不存在满足黑尔配额的联盟通过转向另一组候选人实现严格改进，则该认可委员会是黑尔核心稳定的。每一位选民弃权（不执行）最多两名候选人时，无论候选人数量、席位数量或选民类型数量有无上限，且允许任意正有理数选民权重，我们证明此类委员会必存在。我们的确定性规则通过其缺失集表示委员会，首先最大化两候选人弃权集的加权覆盖，再最大化总弃权发生率。精确覆盖不等式排除席位低于委员会的目标，发生率目标排除全体一致的等规模目标，规模至多为k-2的目标无法改进任何选民。两个实现层面的独立验证者审计重叠的有限网格，符号证明（非该有界枚举）确立定理的无界量词，该论证将补侧覆盖识别为明确定义的偏好域内宽泛参数范围的可处理机制。
英文摘要
An approval committee is Hare-core stable if no coalition meeting the Hare quota can strictly improve by moving to another candidate set. Whether every approval election has such a committee remains open. We prove nonemptiness when each voter disapproves at most two candidates, with no bounds on the numbers of candidates, seats, or voter types. The result also permits arbitrary positive rational voter weights. Our deterministic rule represents a committee by its missing set. It first maximizes weighted coverage of two-candidate disapproval sets and then maximizes total disapproval incidence. An exact coverage inequality excludes targets one seat below the committee. The incidence objective excludes unanimous equal-size targets, while targets of size at most $k-2$ cannot improve any voter. Two implementation-level independent verifiers audit overlapping finite grids. The symbolic proof, not this bounded enumeration, establishes the theorem's unbounded quantifiers. The argument identifies complement-side coverage as a tractable mechanism for a broad parameter range within a sharply defined preference domain.
Comments4 pages, code and other materials are available at: https://github.com/Baymax-ray/approval-core-corank-two
