Econ Papers Daily / 期刊论文
兼容性悖论：基于沙普利的委员会选择中的不可能性
Compatibility paradox: impossibilities in Shapley-based committee selection
摘要
Selecting a committee of size k from a set of candidates involves a delicate balance between maximizing individual excellence and ensuring group compatibility. Recent literature has proposed the k-Shapley value-based committee rule (Dutta et al. 2024), which leverages cooperative game theory to aggregate voters’ approvals of various candidate coalitions into a characteristic function. By selecting candidates with the top-k highest Shapley values, the rule attempts to capture average marginal contributions. In this paper, we build upon this framework by identifying the analytical boundary where candidate-wise aggregation diverges from specific group compatibility. We introduce the “Compatibility Paradox,” demonstrating that because the Shapley value aggregates marginal contributions across all possible subsets, it can occasionally prescribe a committee that voters consider strictly incompatible. We formalize this tension through two impossibility results: first, as an elementary observation that no committee-monotone rule can universally avoid this paradox, and second, as a broader mathematical constraint applicable to any positive weight system (including all regular semivalues). Finally, we propose a constructive remedy, delineating the division of labor between Shapley-based individual scoring and committee-wise evaluation to resolve the paradox.
中文摘要
从候选集合中选出规模为k的委员会，需要在最大化个体卓越性与确保群体兼容性之间取得微妙平衡。近期文献提出了基于k-Shapley值的委员会规则（Dutta等，2024），该规则利用合作博弈论将选民对不同候选人联盟的认可聚合为一个特征函数。通过选择Shapley值最高的前k名候选人，该规则试图捕捉平均边际贡献。本文在该框架基础上，识别出候选人逐项聚合与特定群体兼容性发生偏离的分析边界。我们引入“兼容性悖论”，表明由于Shapley值聚合了所有可能子集上的边际贡献，它有时会指定一个被选民视为严格不兼容的委员会。我们通过两个不可能性结果将这一张力形式化：第一，作为一个基本观察，即不存在任何委员会单调规则能够普遍避免这一悖论；第二，作为一个适用于任何正权重系统（包括所有正则半值）的更广泛数学约束。最后，我们提出一种建设性补救方案，界定基于Shapley的个体评分与委员会层面评估之间的分工，以解决该悖论。