Independent media are central to democratic decision-making, yet recent technological developments, such as social media, pseudonymous identities, and generative AI, have made them more vulnerable to coordinated influence campaigns--usually referred to as Coordinated Inauthentic Behavior. By automatically generating large numbers of similar messages and news reports, such campaigns create an illusion of widespread support, and exploit the tendency of human observers and aggregation mechanisms alike to treat frequency as evidence of credibility or consensus. Clone-robust weighting functions offer a solution to this problem by assigning influence in a way that is insensitive to arbitrary duplication or near-duplication, as measured by a metric. This axiomatic framework rests on three principles: symmetry (equivalent elements are treated equally), continuity (weights vary smoothly under perturbations), and clone-robustness (adding duplicates or near-duplicates does not distort the overall distribution). We provide a general construction of clone-robust weighting functions that applies to arbitrary metric spaces, is entirely independent of the underlying topology, and admits efficient computation. Our approach identifies radius graphs as a natural invariant under cloning, and builds on graph weighting functions that satisfy a basic locality condition. We explore the resulting design space, starting with a simple family that satisfies the core axioms, and then identify explainability as a guiding criterion for navigating this design space. To this end, we introduce sharing coefficients that enable meaningful comparison and interpretation of different constructions, but require additional axiomatic principles. We then consider alternative constructions based on clique-covers, and unveil approaches using clique-partitions that are grounded in information-theoretic principles.

翻译：独立媒体是民主决策的核心，然而社交媒体、匿名身份和生成式人工智能等最新技术发展使其更易受到协调影响力活动的侵害——这类活动通常被称为协调非真实行为。通过自动生成大量相似的信息与新闻报道，此类活动营造出广泛支持的假象，并利用人类观察者与聚合机制倾向于将频次视为可信度或共识证据的特点。克隆鲁棒加权函数通过依据度量标准以对任意复制或近似复制不敏感的方式分配影响力，为这一问题提供了解决方案。该公理化框架基于三项原则：对称性（等效元素平等对待）、连续性（权重在扰动下平滑变化）以及克隆鲁棒性（添加重复或近似重复元素不会扭曲整体分布）。我们提出了一种适用于任意度量空间的通用克隆鲁棒加权函数构造方法，该方法完全独立于底层拓扑结构，且支持高效计算。我们的研究将半径图识别为克隆操作下的自然不变量，并建立在满足基本局部性条件的图加权函数之上。我们探索了由此产生的设计空间：首先构建满足核心公理的简单函数族，随后将可解释性确立为引导该设计空间探索的准则。为此，我们引入了共享系数以实现不同构造间的有效比较与解释，但这需要额外的公理化原则。最后，我们探讨了基于团覆盖的替代构造方案，并揭示了基于信息论原理的团划分方法。