cs.MAOct 26, 2026

Replication or Corroboration? An Axiomatic Framework for Evidential Dependence in Multi-Agent Debate

Authors: Hoang-Loc Cao, Truong Thanh Hung Nguyen, Phuc Truong Loc Nguyen, Vo Thanh Khang Nguyen, Phuc Ho, Hung Nguyen, Duc Pham, Long Tran-Thanh, 

Organizations: University of New Brunswick Canada · FAU Erlangen-Nürnberg Germany · FPT Software Vietnam · Vietnamese-German University Vietnam · 

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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.

Figures & tables

Figure 1. Method overview. (a) Replication and corroboration become indistinguishable once root labels are dropped (Thm. 5 ). (b) Only the lineage quotient qLq_{L} ignores replicas and excerpt splits yet counts fresh roots, and it is the coarsest such key (Thms. 3 – 4 ). (c) Lifting qLq_{L} to QBAFs preserves these guarantees for any semantics (Thm. 1 ), making replication strictly dominated while fresh roots still propagate. Color denotes evidential root.
Representation (key)ReplicaExcerpt splitFresh root
Occurrence multiset222
Content quotient q ⁣Cq_{\!C} (κ,p,s)(\kappa,p,s)121
Content-keyed q ⁣Kq_{\!K} (κ,λ,p,s)(\kappa,\lambda,p,s)122
Lineage quotient q ⁣Lq_{\!L} (λ,p,s)(\lambda,p,s)112
Table 1. Units retained by four representations under three interventions on a role already in the profile.
Figure 2. Only the lineage quotient separates replicas from fresh roots. Toy debate of Ex. 8 under DF-QuAD ( v0=.5v_{0}=.5 , τ=.2\tau=.2 , θ=.5\theta=.5 ), one added report per column. Cells give the topic score, colored by whether the judge meets the target (replicas neutral, fresh roots move the score in their sign). An argumentation graph with one supporter and one attacker of a claim, beside a table of topic scores for six judges under four single-report interventions: relay, excerpt, fresh attacker, and fresh supporter.
JudgeCDRSS 8RFR 8FLGMinGFASR
Vote.1818.2723.4582.0752.05001.0000
Occurrence DF-QuAD.0000.0677.0932.0298.0013.1922
Max-QuAD.0448.0000.0000.0000.0000.0000
Content quotient.0000.0000.0000.0000.0000.0000
Lineage quotient.0000.0000.0000.0298.0013.0000
Table 2. Exhaustive structural audit. Target: CD=RSS8=RFR8=FASR=0\mathrm{CD}=\mathrm{RSS}_{8}=\mathrm{RFR}_{8}=\mathrm{FASR}=0 and MinG>0\mathrm{MinG}>0 . Bold marks joint satisfaction.
JudgeCDRSS 8RFR 8FLGMinGFASR
Vote.0187.0572.0703.0219.00001.0000
Occurrence DF-QuAD.0000.0114.0689.00881.1 ⁣× ⁣10−81.1\!\times\!10^{-8}.9800
Max-QuAD.0278.0000.0000.0000.0000.0000
Content quotient.0003.0000.0000.0000.0000.0000
URL quotient.0002.0000.0000.0000.0000.0000
Lineage quotient.0000.0000.0000.00881.1 ⁣× ⁣10−81.1\!\times\!10^{-8}.0000
Table 3. Matched audit on 277 AVeriTeC-derived profiles. Same target as Table 2 .
Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

JudgeCDRSS 8RFR 8FLGMinGFASRnFn_{F}
Vote.01867 [.01408,.02373].05724 [.04294,.07196].07032 [.05292,.08873].02194 [.01648,.02766].000001.000 [1.000,1.000]50
Occurrence DF-QuAD.00000 [.00000,.00000].01137 [.00894,.01399].06892 [.05114,.08733].00880 [.00710,.01069]1.13 ⁣× ⁣10−81.13\!\times\!10^{-8}.980 [.933,1.000]50
Max-QuAD.02785 [.02546,.03035].00000 [.00000,.00000].00000 [.00000,.00000].00000 [.00000,.00000].00000.000 [.000,.000]61
Content quotient.00028 [.00000,.00075].00000 [.00000,.00000].00000 [.00000,.00000].00000 [.00000,.00000].00000.000 [.000,.000]50
URL quotient.00020 [.00000,.00060].00000 [.00000,.00000].00000 [.00000,.00000].00000 [.00000,.00000].00000.000 [.000,.000]50
Lineage quotient.00000 [.00000,.00000].00000 [.00000,.00000].00000 [.00000,.00000].00880 [.00710,.01066]1.13 ⁣× ⁣10−81.13\!\times\!10^{-8}.000 [.000,.000]50
Appendix
Table 4. AVeriTeC audit with claim-clustered 95% bootstrap intervals. MinG is the observed finite-position minimum, and nFn_{F} is the judge-specific FASR denominator.
StatisticValueStatisticValue
Claims277Supported / Refuted127 / 150
Reports711Support / attack152 / 559
Reports per claim2.57Mixed-sign claims47
Content-Q changed3URL-Q changed2
Fresh positions711FASR-eligible claims47
Appendix
Table 5. AVeriTeC profile statistics after the stated filters.
ConditionClaimsPos.FLG [95% CI]MinG
NLI thr. .50277737.00833 [.00670,.01018]1.13×10−81.13{\times}10^{-8}
NLI thr. .60277711.00880 [.00710,.01066]1.13×10−81.13{\times}10^{-8}
NLI thr. .70237601.00655 [.00510,.00819]1.36×10−81.36{\times}10^{-8}
Fixed str. .50277711.05132 [.04746,.05526].001953
Appendix
Table 6. Sensitivity of the AVeriTeC lineage-quotient audit. FLG is reported with a claim-clustered 95% bootstrap interval.
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