Breaking the Illusion of Artificial Consensus: Clone-Robust Weighting for Arbitrary Metric Spaces

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.