Abstract
In multi-agent debates, matching reports can arise for two different reasons: agents may repeat the same evidence (replication), or they may provide separate evidential roots that support the same claim (corroboration). A judge must distinguish these two cases. Counting report occurrences gives extra weight to relays, paraphrases, alias resubmissions, and excerpt splits, while merging all matching content avoids this only by also removing genuine corroboration. We formalize this tension as a minimal judgment game in which acquiring new evidence is costly, but replication is cheap. We show that root replication invariance (RRI) is exactly threshold-uniform replication immunity. Under RRI, replication-only deviations cannot change the verdict, and positive-cost replication is strictly dominated, whereas occurrence-sensitive and content-keyed judges admit profitable deviations. We also establish an information boundary: if a judge's observation interface cannot distinguish a replica from a matched fresh root, no judge can both ignore the replica and respond strictly to the fresh root. To preserve this distinction, we introduce the lineage quotient, which removes wording, identity, occurrence multiplicity, and arbitrary root names while keeping distinct roots separate. On orbit-connected domains, it is the coarsest representation sufficient for every deterministic judge invariant to replication and root-label renaming. We further lift this construction to quantitative bipolar argumentation frameworks (QBAFs), characterize strict fresh-root response, prove its propagation along sign-consistent paths under DF-QuAD, and derive a tight closed-form response modulus. Exhaustive audits over 28,224 direct-star profiles, 2,052 multi-layer DAGs, with matched interventions on 277 AVeriTeC-derived profiles, show the predicted separation between replication and corroboration under a supplied partition.
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URL
https://arxiv.org/abs/2610.36151
